Basically, yes.
The best clue that they would have had that 'something was up' was the use of the three prototype heavy tank types (SMK, T-100, KV) against Finland. These were all competitors for the role of new heavy tank, and though the decision had already been made to go with the KV, the opportunity to get a little real-world experience (and, frankly, help out with knocking out those upstart Finns who didn't want to give up) was worth sending the tanks up to partake.
Indeed, the SMK was immobilised by a Finnish mine and captured, there are plenty of pictures of the Finns climbing over the thing, but it was too heavy to drag away. Still, given that Germany and Finland were on pretty reasonable terms at the time, the Germans would have certainly been told "Guys, the Russians are using big tanks with 7.5-cm -ish guns, and stupid amounts of armor". But that would have been it.
The existence of the KV didn't come as much as a surprise as the T-34. Indeed, part of the reason that T-34 doesn't get the 'credit' it deserves for being around on Day 1 is that oftentimes Germans were sending back pictures of T-34s captioned as KVs. If you think about it, it makes sense. A German soldier sees a new, unfamiliar tank, bigger than most, with a pretty reasonably large gun, and he knows rumours of the "KV", he's going to assume what he's looking at is, in fact, a KV if nobody mentions "T-34" to him.
In reality, T-34s were around on Day 1. Also in reality, they were of questionable success. Indeed, after a month, the Soviets had lost more T-34s than they had started with: 935 on Day 1, 526 replacements, 1,303 lost by 01AUG, with 158 still on the books. Stories of how a single KV held up Sixth Panzer for 8 hours or whatever were the exception, not the rule.
What was happening was that the Germans simply did what they had done the previous year in France when coming up against heavily armored vehicles. Proper maneuver and use of combined arms. The Western Allies would do exactly the same thing to the big German tanks three years later.
That's not to say the vehicles didn't make an impression, of course. Any soldier wants 'easy mode', and it was awfully complicated to have to go around the side, or call in supporting assets to kill these things. The vehicles caused the adoption into service of the long 5cm gun on Panzer III and 7.5cm gun on Panzer IV. Of interest, Guderian (I believe it was, I'm working from memory here) was interested in the long gun more for the purposes of morale than practicality. He recommended that a few tanks in the battalion be equipped with a 'giant-killer' gun, to give the troops confidence should they encounter one, but keep more suitable guns on the majority of the tanks.
Yes, Germany was unaware of any Soviet tanks. Germany published an identification guide on Soviet AFVs shortly before the invasion. The guide included the BA-11 (called BA-Ford in the guide), T-37, T-38, Vickers-Armstrongs T-26A (two-turreted T-26), Vickers-Armstrongs T-26B (single-turreted T-26 with a 45 mm gun), Vickers-Armstrongs T-26B flamethrower tank (KhT-130), Vickers-Armstrongs T-26C (T-26 with a sloped turret and turret platform), BT (just one type is specified in the guide, looks like a mix between the BT-2 and BT-7 with a conical turret), T-28, T-35A, and a very interesting tank called the T-35C.
The T-35C is actually the SMK tank that was disabled in Finland and even though the Finns couldn't evacuate it, it was definitely inspected and photographed. Due to the shape of the tank and its multiple turrets it wasn't hard to ascribe a relation to the T-35, hence T-35C. Don't ask me what the T-35B was supposed to be, perhaps the T-35 with sloped armour.
So not only were the Germans not aware of the T-34, they didn't know about the latest development in Soviet tank building in general: no KV-1, no T-40 or T-50, etc.
As for the reaction, the Germans noticed the T-34 in the first days of the war. On June 23rd, 1941, a drawing labelled "Panzerkampfwagen Sudwesteingang Razdechow" quite clearly depicting a T-34 tank with an F-34 gun was made by the 297th Infantry Regiment. The Germans estimated this tank to weigh 35-40 tons. There wasn't really much time for evaluation, but after reports of "superheavy enemy tanks" the Germans brought up 88 mm AA guns that worked about as well as they did against Matildas in France. Various memoirs by German generals remark on the debut of the T-34 tank anywhere between July and October of 1941, so it appears that they didn't make much of an impression on high ranking commanders, but were quite noticeable at the tactical level. For instance, one of Guderian's subordinates wrote:
In our battles, the 4th Panzer Division often fought with Russian heavy tanks. At first they appeared rarely and could be stopped by massed artillery fire or bypassed.
...
After we took Orel the Russians started using heavy tanks en massed for the first time.
...
For the first time in the campaign in the East, the supremacy of Russian 26 and 52 ton tanks over our Pz.Kpfw.III and IV was absolute. Russian tanks form a semicircle and open fire at 1000 meters from their 7.62 cm guns that combine incredible penetrative power and high precision. Our 5 cm tank guns only penetrate weak spots in ideal scenarios from 50 meters.
...
In addition to superior effectiveness of the armament, the 26 ton Christie tank (T-34) is faster and more maneuverable, its turret traverse mechanism has undeniable advantages. The tank's wide tracks allow it to ford rivers that are inaccessible to our tanks. The ground pressure is much lower than that of our tanks, and despite its heavy weight the Russian tank can traverse the same bridges as our tanks can.
The exceptional diesel engine deserves attention.
...
The high energy and fighting spirit characteristic of our attacks will wane and be spent due to a feeling of inadequacy. Crews know that they can be knocked out by enemy tanks from a large distance, but they can only have a minimal effect despite the use of special ammunition at close range."
The report is quite long and lists some solutions, including using as many captured T-34s and KVs as possible and building their own clone of the T-34 tank, or at the very least transplanting Soviet 76 mm tank guns into the turret of the Pz.Kpfw.IV tank. As you can see, the effect of the tank on German troops was quite high.
The tank was notable enough for the German Panzer Commission to visit the front lines in November of 1941 and examine some captured samples. This inspection had some direct impacts on German tank development. For instance, Krupp quite liked the technique of using curved armour plates used to make the front of the T-34's hull and turret, and used a similar solution on some of its new designs. The concept of a large turret bustle was also copied. It is often said that the Germans learned about sloped armour from the T-34, but it appears in earlier German designs, nevertheless sloped armour was introduced in German medium and heavy tanks only after inspecting T-34 tanks. Heydekampf also listed a large overhanging gun and large road wheels as features lifted from the T-34, but these features were seen in German tank designs before this inspection.
There are also some exaggerations about the effect of the T-34 tank on German design. For one, the VK 30.01 (D) wasn't a copy of the T-34 at all. Some of the layout decisions were similar, but the internal components were previously tested on the VK 20 vehicles. Second, the V-2 engine is rumoured to have jump-started German diesel engine development, but Daimler-Benz had their own diesel engines used in tanks even before that, and it didn't really seem to have much of an impact on engine design. Finally, there are some who claim that the T-34 resulted in the development of the Tiger as a reaction to the design. This isn't true, since the requirement for 100 mm front armour and an 88 mm gun predate the German encounter with the T-34. The Panther can definitely be called a reaction to the T-34 tank, as the Germans stopped development of the 20 ton medium tank class and started working on the 30 ton medium tank class after having examined the Soviet tanks closely.
Sources:
http://www.tankarchives.ca/2015/05/german-intel-red-army-tanks.html
https://www.tankarchives.ca/2019/09/t-34-and-kv-1-first-intel.html
A. Ulanov, D. Shein, Perviye Tridtsatchetverki, Tactical Press, Moscow, 2013