That's entirely false. In fact it's an incorrect retelling of an already entirely false allegation (Sweden aiding the invasion of Norway).

First off just the allegation makes no sense on any level; Sweden, Denmark and Norway all declared themselves neutral at the outbreak of the war, September 1 1939. All three countries had been democratic for a century or more by that time. All three were lead by Social Democratic governments, who'd all polled at about 45% of the vote in their respective last elections prior to the war. On the other hand, Nazi and Nazi-aligned parties combined did not amount to more than 2% of the vote in any of the Scandinavian countries. All the Scandinavian countries had strong trade relations with Germany, which is something that goes back to the Middle Ages, but after the 19th century's strong Scandinavianism movements, relations between the Scandinavian countries was as warm as ever.

So without even going into details, right on the face of it, just the accusation makes no sense on any level, really. Why would Sweden ally itself with Germany in war of aggression against neighboring countries? Neighboring countries that the Swedish public felt more friendship and kinship? And against Sweden's own interests as an occupation of Norway and Denmark would make an occupation of Sweden much easier? Why wold the Social-Democratic government of Sweden (or later, Social-Democratic-led coalition government) sympathize with Facists with whom they not only had nothing in common with politically, but who'd imprisoned their German comrades and put them in concentration camps? (and some of the Swedish SDP leadership personally knew leaders of the German party)

So, in short Sweden was not a friend of Germany. On the contrary, from the outbreak of the war, Sweden's main concern was a German invasion of Sweden. As the Swedish ambassador to Berlin, Arvid Richert, put it in a secret telegram to the government in November 1939:

.. our country's concerns are now so threatened, that one must constantly be aware of the risk of conflict with Germany, and everything must be done within the realm of the possible to prevent such [a conflict]

And that's a representative opinion for the government position. Sweden did not side with Germany and did not want to help the German war effort. However, the country forced to walk a tightrope during the war. Sweden was still economically critically dependent on imports of coal from Germany. The ability to export/import goods from Allied nations was controlled by Germany as well, as they controlled Norway, Denmark and had mined the Skagerrak strait. (a major reason for Germany's invasion of Norway was precisely that: it gave Germany control over Swedish exports without necessitating an invasion of the actual country) I've elaborated a great deal on all this in a post here and /u/vonadler covered much of the same ground in an excellent post here.

Th image that Sweden voluntarily aided Germany is a distortion that's usually based on two facts, which are the most repeated ones about Sweden's involvement in the war. The first being Sweden's exports of iron ore to Germany. As said in that post this was technically not a breach of neutrality, as the Allies and Germany had signed a war trade agreement with Sweden, permitting the export of ore.

The second, which was a violation of neutrality, was that Sweden agreed (under threat; the threats were constant) to allow unarmed German troops (although a couple of exceptions to that occurred) on leave to pass through Sweden on trains to get to Germany and back from the occupied Norway. This was after the invasion of Norway was completed. It's a widely known thing - not least in Sweden - because it was extremely controversial and publicly known. But it was controversial precisely because the Swedish public had little love for the Germans, especially after invading Norway and Denmark. Another indicator for that perhaps is the fact that relatively few Swedes left to volunteer for the SS in Germany. By latest count (by Gyllenhaal) as few as 180. Even the highest estimates are under 500. That's as opposed to about 6,000 from Denmark and and just under 6,000 from Norway who fought for their occupiers. Or you could compare to about 2,000 from neutral Switzerland. Or the 9,500 swedes who volunteered for Finland in the Winter War. However you cut it, there was little popular enthusiasm for helping the German war effort, even with the Germans doing their best to change that fact by publishing Swedish-language propaganda in Sweden, such as the magazine Tyska Röster ('German Voices'). The German embassy staff in Stockholm swelled to hundreds of spies during the war.

Anyway, in the telephone game of misunderstood historical facts the German trains story goes from "Sweden wasn't neutral - they let Germans pass through the country" to "Sweden helped Germany, they let German troops go to Norway through Sweden" to "Sweden was an ally of Germany and let them invade Norway though Sweden" to - now apparently - "Sweden helped Germany invade Denmark", adding quite a twist since Sweden isn't even between Denmark and Germany.

The Swedish government was no more aware of the impending invasion of Norway and Denmark than the Norwegians or Danes were - and had no reason to be. That's simply a fact, there's no evidence to the contrary. Given the invasion of Denmark was over in 6 hours, Sweden probably wouldn't have had a theoretical chance of helping Germany there even if you were to entertain the idea that they'd want to for some reason.

I wont' go into all details here as the former post I did that I linked to did so, but suffice to say that Sweden took many actions against German interests during the war; breaking German codes and wiretapping their communications, leaking some information to the allies, the rescue of Denmark's Jews, and the covert training of thousands of Norwegian and Danish resistance men.

The source of much of the criticism is actually Sweden itself though. As other countries of Western Europe had a critical re-examination of the crimes of the past in the 1960s and 70s. In Sweden, that lead to an increased focus on and criticism of Sweden's concessions to Germany during the war. In the popular narrative, Sweden's status was almost reduced to that of a tributary state (or Mitläufer perhaps) based on arguments that have been criticized by historians (e.g. here by Alf Johansson) for being quite 'presentist', that is, made from a present day perspective and knowing what we know now. Or they are simplistic readings of complicated situations, such as Sweden mining parts of its Baltic coast against Soviet submarines. That was something the Germans wanted, but does it make it a 'concession' to them given that it was also perfectly legal and legitimate thing to do for Sweden's own defense? The most grievous violation of Swedish neutrality was the concession of allowing the armed German Engelbrecht division pass through Sweden from Norway to Finland, in order to aid the now-German-allied Finland against a Soviet attack. The demand for this precipitated the "Midsummer Crisis" as the Swedish government was deeply conflicted about the demand, which was pushed through by the king's (alleged) threat of abdicating if the troops were not allowed to pass. So in that situation you had German threats, the threat of a constitutional crisis, and the complicating matter of Sweden's strong sympathies for Finland and against the Soviet. (Swedish aid to Finland in the Winter War of 1939-40 had even exceeded the defense budget)

In summary: Sweden was not an ally of Germany. Neither the Swedish government nor public had much love for the Nazis. Sweden did not aid the invasions of Norway or Denmark. But they did however take actions after those occupations that violated neutrality and passively helped the Germans. But Sweden also violated neutrality with actions against German interests. Although such narratives abound in popular descriptions, it's also much too simplistic to describe Sweden as being a sort of involuntary client state to Germany. (much less an active, voluntary one) There's not going to be any end to woulda-coulda-shoulda debates about whether Sweden could've done less or pushed back more and so on, often from a presentist angle. But there's certainly no debate that the concessions made were done out of fear of German invasion or military retaliation.

/u/Platypuskeeper have given you a good answer on the first part of your question, so I'll focus on "Rädda Danmark" (save Denmark).

"Rädda Danmark" was an operation intended to attack the Germam troops in Denmark should they refuse to surrender or even take Danish civilians hostage in order to force better surrender terms than unconditional. It was mostly the navy's pipe dream. Planning did go ahead, headed by the commander of the Swedish navy, Admiral Fabian Tamm. However, while the navy certainly could dominate the Danish Straits and sweep any mines, the Swedish armed forces completely lacked any kind of landing crafts - transport was to be done in converted fishing trawlers - slow and small wooden ships completely without protection for the men in them.

Lieutenant Colonel Karl Wärnberg, the army officer assigned to the planning of "Rädda Danmark" kept pestering Tamm with the same question over and over again - "How do we get ashore?". As Tamm could not answer that to army satisfaction, the plan was eventually shelved - it did get get decently far though, as on the 5th of May 1945 there were troops and ships assigned to all parts of the plan and a potential go ahead date had been set to the 18th of May, despite the army's resistance.

The original plan called for the Swedish coastal artillery to dominate the Danish Strait and destroy its German counterpart in Denmark, supported by the floating battery (ex-armoured ship) HMS Äran and the armored ships HMS Tapperheten and HMS Oscar II would provide mobile fire support together with a squadron of smaller ships which would protect the roughly 1 200 ships (mostly fishing trawlers and even smaller wooden "assault boats" the army used for river crossings).

Coastal artillery assigned to the operation:

South of Malmö:

12x15,2cm m/37 and 21cm m/42 mobile artillery guns (the 21cm was mobile but not tactically so, which the 15,2cm was).

HMS Äran (the armoured ship HMS Äran's engines were worn out and she could not move by her own power, but she was towed and used as a floating coastal battery. she had 2x1x21cm and 6x1x15,2cm).

At Landskrona (about halfway between Malmö and Helsingborg): 4x15,2cm m/37 guns.

North and south of Helsingborg:

16x15,2cm emplaced heavy coastal artillery guns (4 in each Batteri Helsingborg, Batteri Viken, Batteri Trelleborg and Batteri Ystad).

9x21cm m/42 guns (3 batteries of 3 guns each)

18x15,2cm m/37 (2 battalions of 9 guns each)

The mobile guns were from I/KA2 and I/KA4 (KA = Kustartilleri, coastal artillery regiment).

HMS Oscar II and HMS Tapperheten were to be protected by 7 destroyers, 6 MTBs, 16 minesweepers and 6 patrol boats.

For naval support and taking out enemy ships most of the Swedish navy would be available, including the three Sverige class armoured ships and 10 destroyers.

Land forces included 3. Army Corps, consisting of 2 infantry divisions (I. and XI.), 1 armoured brigade (8.), 1 motorised brigade (7.) and the Danish "Police" brigade were to be transported to Sjaelland and 1 infantry regiment (I41) to Bornholm.

Image in Swedish with the general plan.

The general plan for Bornholm.

The general plan, original Swedish document - in Swedish.

An infantry squad in a fishing trawler as intended to use in the landings. Note the "assault boat" that Swedish infantry used for river crossings loaded on top of the fishing trawler. These were to be used to get some of the troops ashore. They were unarmoured wooden craft. Bicycles loaded on an "assault boat". An AT gun and its crew loaded on a trawler.

The Swedish force were to be supported by a majority of the Swedish air force and would count some 60 000 men and 6 000vehicles, including ~200 tanks. The Germans had roughly 28 000 men at Sjaelland in May 1945, a large part of them 3rd line garrison forces. Their coastal artillery was limited to:

At Helsingör:

1x10,5cm coastal gun

1x15cm coastal gun

At Hesbjerg:

4x15cm coastal guns

At Hornbaek:

4x12cm coastal guns

At Nivå:

4x7,5cm guns

At Copenhagen were also the heavy cruiser Prinz Eugen and the light cruiser Nürnberg along with 4 destroyers, some minesweepers and other light craft, but it is entirely possible these ships lacked the fuel to sortie and meet the Swedish navy.

As you can see from the images, it is easy to understand why the army had serious concerns about the whole operation - while the trawlers are just a bit better than the barges the Germans intended to use for Operation Sea Lion, they are still woefully unprotected against any enemy resistance.

"Operation Rädda Danmark" was really only viable if the Germans were already surrendering, and if they were, it would not be needed.

"Rädda Norge" (which I will try to write about below), was far more viable.

Sources:

Original plan in Swedish (linked above).

Den svenska d-dagen, article by Per-Anders Lundström in SMB's membership paper "Pennan och Svärdet".

"Rädda Danmark" article by Dasnk Militaerhistoriskt selskab (noe defunct).

En svensk tiger by Sven-Åke Bengtsson.

Sorry about the long delay, here's the post on the planned Swedish invasion of Norway 1945.

Operation Rädda Norge (Operation Save Norway) was the more ambitious plan, and cetainly the more realistic one compared to Operation Rädda Danmark.

The Swedish legation (embassy in modern terms - before 1946, only grand powers had embassies led by ambassadors to each other, while smaller countries to each others and grand powers to smaller countries had legations or missions headed by envoys, ministers or chargé de affaires) in Germany reported in late Autumn 1944, especially the Military Attaché Curt Juhlin-Dannfelt, that Hitler was in such bad health that he could only focus for about 15 minutes in a stretch and that Göring was less and less interested in military matters and that Himmler now seemed like the strong man in Germany. Himmmler's masseur Kersten was a Swede, and he reported to the Swedish foreign ministry on the inner workings of Himmler and his closest associates when he visited Sweden, reinforcing these ideas. Himmler seemed like a man that would fight to the last rather than surrender, and the Swedish society and military would have to act in accordance with that.

Sweden had since mid-1943 trained roughly 17 000 Norwegian refugees as "Rikspoliti" ("Realm Police") and "Reservpoliti" ("Reserve Police"), in reality these so-called "police" formations were fully trained and equipped as regular Swedish infantry, including mortars, light AA guns, AT-gunsm machine-guns, submachine-guns and other small arms. By 1945, there were 8 "Rikspoliti" companies (motorised infantry heavily equipped with automatic arms along the line of Swedish military police) and 9 (with 1 more being set up) "Reservpoliti" battalions (regular infantry), plus support elements, 1 engineer company and 1 artillery battery (equipped with the 10,5cm guns the Norwegian 1. Division had brougth with them when they crossed the border to be interned in April 1940). In one sense the Norwegians were even better equipped than their Swedish counterparts - they had access to British PIAT infantry AT weapons, brought by the British (perhaps aptly names) Gay Viking class gun motorboats that crossed the North Sea Winter 1944-45 to bring back high-quality ball bearings from Swedish firm SKF.

Some of the Norwegian "Reservpoliti" battalions had already gone into action, as the Germans retreated away from Finns and Soviets in Finnmark in northern Norway. Fearing for the civilians and perhaps a possible Soviet occupation of the territory, the Norwegian government-in-exile requested that Sweden allow the usage of the "police" troops. Sweden accepted, and two "Rikspoliti" companies and two "Reservpoliti" battalions headed into Finnmark to restore order, protect the civilians and make sure both Germans and Soviets kept out. They were supplied by mostly American C-47 Dakotas from Luleå - using a depot that had ironically been used by the Germans to store horse fooder and food for their troops in Finland before.

With that as a background, let me get on to the actual operaton.

Swedish military intelligence, C-byrån (the C-bureau) led by Colonel Carlos Adlercreutz had extensive contacts with the Norwegian resistance and civilian officials in Norway such as police men, administrators, toll officials, harbour pilots and clearers, railway officials and so on and had a very good idea on the strength of the German forces in Norway - it was estimated at 100 000 frontline troops and roughly 80 000 third line or rear area men, mostly Kriegsmarine and Luftwaffe rear area personell. The real numbers were around 102 000 frontline troops and 206 000 third line or rear area men, for a total of 308 000. It seems like in what counts, the frontline soldiers, the Swedish intelligence was accurate.

Sweden also acquired information on the placement of German troops and the activity in the staff of the German commander in Norway Böhmer. As an example, when the German 25. Panzer-division in June 1943 moved from the Oslo area to the Trondheim area (before leaving Norway in August 1943), its new position shows up in Swedish staff reports 2 days after the movement finished. Böhmer seem to have held a kriegsspiel (war game) on a Swedish attack which turned up negative results for the Germans in NOrway on the 2nd of May 1945 - something which figures in the Swedish documentation on a possible invasion.

The Swedish miliary planning for a conflict with the Germans in Norway was initially extremely defensive, intending to use the sparse roads and dense forests to use Finnish Motti tactics against invading German forces. However, from early 1942 and onwards the planning also included an attack towards Mo-i-Rana, a port in northern Norway between Narvik and Trondheim, where Norway is at its narrowest, as it was both a decent port, connected by road to Sweden and close to impossible to reinforce by land for the Germans due to lack of infrastructure. The intention then was to open a port through which Western Allied support for Sweden could come through.

Churchill let Sweden know through the Swedish minister in Finland, Beck-Friis that an Western Allied action against the Germans in Norway was not possible due to the lack of tonnage for shipment in February 1945. If Sweden wanted to attack the Germans in Norway, SHAEF (Supreme Headquarters Allied Expeditionary Forces) was all for it, but could not promise any substantial support.

The Swedish plan included a 3-pronged attack against Oslo by III. MILO (Militärområdet, the Military Area) and 1. Armékåren (1. Army Corps) while II. MILO would launch an attack from Härjedalen towards the area south of Trondheim and VI. MILO attacked across the border to take Mo-i-Rana.

From north to south, the Swedish forces would be:

VI. MILO (attacking Mo-i-Rana).

1 infantry division (XV. Fördelningen), 1 infantry regiment (I19), 1 infantry battalion (II/I31), 1 Jäger/Special forces battalion (XIX. Kårjägarbataljonen), 1 corps artillery battalion (XII. Kårartilleridivisionen), 1 AA battalion (IX. Kårluftvärnsdivisionen) plus various support units, including 2 infantry companies, 1 AT company, 1 motorised military police company, 2 engineer companies, 3 road construction companies and 8 independend jäger/special forces platoons.

II. MILO (attacking south of Trondheim).

1 infantry division (II. Fördelningen), 1 infantry battalion (II/I44), 1 jäger/special forces battalion (V. Kårjägarbataljonen) plus support elements including 1 engineer company and 7 indpendent jäger/special forces platoons.

1. Armékåren (attacking towards Oslo from the east).

5 infantry divisions (Iv., XII., XIII., XIV. and XV. Fördelningen), 2 armoured brigades (each had 185 tanks), 1 assault gun battalion (18 assault guns), 5 corps artillery battalions (III., IV., VI., VII. and VIII. Kårartilleridivisionen), 3 AA battalions (Kårluftvärnsdivisionen Lv 1, II. and VIII. Kårluftvärnsdivisionen), 2 infantry battalions (I and III/I10), 1 jäger/special forces battalion (II. Kårjägarbataljonen) plus support elements including 5 motorised military police companies, 6 engineer companies, 14 construction/road building companies, 2 field replacement battalions, 12 field replacement companies and 6 independent jäger/special forces platoons.

III. MILO (attacking towards Oslo from the southeast).

1 infantry division (III. Fördelningen), 1 infantry battalion (I/I46), 1 corps artillery battalion (II. Kårartilleridivisionen), 1 AA battalion (VI. Kårluftvärnsdivisionen) plus support elements including 2 engineer companies, 3 construction/road building companies, 3 motorised military police companies, 6 field replacement companies and 5 independent jäger/special forces platoons.

Reserves

2 infantry divisions, 1 armoured brigade (with 185 tanks), 1 motorised brigade, 1 bicycle brigade, plus 6 motorised infantry companies and 7 infantry battalions from the Norwegian police troops.

This is roughly 250 000 men and 370 tanks, that was to be supported by the whole of the Swedish airforce, roughly 440 planes at this time. One should note that the Swedish forces while untested in real battle are well supplied, fresh, have a high morale and consists of the best recruits and with extensive tactical, operational and strategic mobility.

Continued below.