Yes Nils Grabbe existed and did stuff during Vasa's War of Liberation against Denmark. (1520-1523) The Grabbe family (and their estate Grabbacka outside Raseborg, whose ruins are there still) are well attested as low nobility in the region. For instance there are several letters from the early 1500s mentioning his father Måns (or Magnus) Grabbe as häradshövding_ (Fin: kihlakunnantuomari) in 1500, over the eastern hundred (Sw: härad, Fin: kihlakunta) of Raseborg.

To recap: Christian II didn't just try to conquer Sweden but succeded in doing so in 1520, even if he did not hold it for long. That culiminated with him having himself coronated as king in Stockholm, and the ensuing "Stockholm bloodbath" where Christian executed upwards of 100 people, mainly noblemen, who'd been members (or suspected members) of the anti-union Sture party. He'd taken control over the country, but Vasa had begun his organized rebellion against Christian within months.

Now, Sweden and Finland were administratively divided into 'castle counties' (Sw: slottslän, Fin: linnaläänit), regions ruled from a castle, by a governor (Sw: fogde, Fin: vouti) appointed by the king as the direct representative of the crown. Conquering the country meant taking those castles.

For Finland's part (not counting Åland) this consisted of 8 castles: Åbo (Turun linna), Tavastehus (Häämen linna), Raseborg (Raaseporin linna), Nyslott/Olofsborg (Savonlinna/Olavinlinna), Kumo (Kokemäen linna), Borgå (Porvoo), Korsholm (Korsholman linna), Viborg (Viipurin linna).

There were also some bishop's castles; of note here is the one belonging to the Swedish archbishop at Almarestäket, which was besieged by Sture forces due to Bishop Trolle's suspected loyalty to Christian. This siege in 1517 was the pretext for Christian's invasions. In Finland's case the most significant one was Kustö castle (Kuusiston piispanlinna), home of the Bishop of Turku/Åbo. Most bishop's castles were destroyed by Gustav Vasa, not as part of his war of liberation but afterwards as part of his establishing the Reformation and essentially ending the Church as an independent power. (and he didn't want to risk anyone else using them to build power either)

So Vasa set about gathering men and laying siege to castles; Västerås castle was for instance under siege for a year before falling in 1522. Meanwhile, Nils Arvidsson and Erik Fleming were sent with forces to Finland to lay siege to Turku castle in November 1521, where the Danish fogde Tomas Lebe resided. They were aided in this by the local forces hostile to Christian II, such as Turku bishop Arvid Kurck (Arvi Kurki), Nils Grabbe and their men. The siege was broken by the forces of the danish commander Søren Norby in May 1522, and the Swedish forces had to retreat, as did the bishop. Vasa wanted to make him archbishop for his proven loyalty but Kurck died in a shipwreck on his way to Sweden. Grabbe, on the other hand, decides to stay and fight, and it's now he supposedly starts his partisan career of raiding the danes on the coast. This (and most of the details above) according to the chronicle of Peder Svart.

Søren Norby continued to Raseborg, where his brother-in-law Tile Giseler was under siege and managed to liberate him as well, securing Danish rule in much of Finland, for a time, and was rewarded by king Christian with the abandoned castle of Kustö.

Meanwhile, according to Peder Svart's chronicle, Grabbe was doing hit-and run attacks in skerry-boats (skäribåtar) at Raseborg, Kumo and Borgå. He was clever, catching the danes in their sleep, and boarding up doors before setting buildings on fire, often killing 2-300 in one go, says Svart. When there was risk they'd overwhelm him, then he'd flee "to Reval or other places in Livonia".

Norby would some months later attempt to liberate Stockholm from Vasa's siege as well but was hit but unseasonably cold weather in the Stockholm archipelago and his ships were stuck in the ice, and attacked by the Finnish nobleman Erik Fleming's naval forces, although he managed to escape with few losses. Stockholm falls to Vasa's forces in June 1523, but much of Finland still remains in Danish hands, and Vasa's German mercenary forces are sent over in August.

Kustö, with Norby and most of his troops absent, surrendered in a day. Turku castle held out 12 days, after which the Swedish forces split off to take the remaining castles at Häämenlinna, Raseborg, Savonlinna, and Viipuri, and Grabbe was delegated the task of retaking Viipuri. Which is supported by a letter of Octobor 10, 1523 (DF 6134), where Nils Grabbe and several other commanders (e.g. Erik's brother Ivar Fleming, fogde of Kumo, retaken in 1521) negotiated the surrender by Danish fogde Roloff Mattsson of Viipuri and Savonlinna castles. Thereby ending Danish control over Finland.

Grabbe's further career as governor of Raseborg and later Viipuri is more well documented. But the main documentation of his supposed privateer /partisan career is Peder Swart's chronicle. (text in early modern Swedish, chapters #43-44, #49, #67) Which does not go into great detail though, in fact I've repeated most of what it says here.

Now, Svart's chronicle was written around 1560, quite a while after Grabbe's supposed exploits but still within living memory. It was commissioned by Gustav Vasa as an anti-Danish propaganda piece. Some stories are pure fabrications; most infamously it invented the stories of Gustav Vasa in Dalarna, in a series of episodes where Vasa continually outwitted a delegation of Danish troops out to get him. Although these were commonly taught in schools as 'history' (or 'stories from history') until the early 20th century they're not considered historical at all these days.

So it's pretty likely Grabbe's exploits as a partisan-pirate hero were overstated. It's hardly likely he attacked 'Kumegård' (Kokemäki), which as said was already back in Swedish hands by then, and a bit out of the way from the other places. That said, it's not impossible it had a kernel of truth to it - there's a letter from August 4, 1523 (DF 6123) registers Nils Grabbe arriving in Reval (Tallinn) with the royal ship Ugglan, to deposit wreckage goods from off the Finnish coast with the city's aldermen until the king can decide who the rightful owner is.

What you've read seems to be a fictional elaboration on Svart's embellished story. There's no record of a ship named something like "Queen of the Night", much less Grabbe having one; as said, there is a record of Grabbe commanding "His Majesty's ship Ugglan" ('the owl'). Perhaps the author was relying only on Svart as a source as Svart doesn't mention any ship names. Nor a record of "Fyen's swan" which might be based off Lybska Svan ('the swan from Lübeck'), the name of Vasa's flagship. (although politically nonsensical since Sweden was friendly with Lübeck at the time while Fyen, modern Fyn, is a Danish and thus enemy place)

Nor is there any record of a "Jens Staxrud". Even Google only turns up that book. Which, btw, seems to call him junkkeri - (Swedish/English junker), rather than jarl which are quite different titles. 'Junker' is more expected since 'jarl' was an obsolete medieval title by 1500 but 'junker' was quite common as a derogatory term for a nobleman at the time; e.g. Junker Tomas was the Swedish nickname for the aforementioned Tomas Lebe.

The name "Staxrud" doesn't really make sense as a Swedish name of the time - ordinary Scandinavians didn't have family names at this point in time, just frälse (nobilty and clergy), and those names were typically what was on their coat of arms. Vasa for instance had a vase (a vase-shaped sheaf of grain) on his. But "Staxrud" (or 'Stacksrud' or whatever spelling) isn't an object; "-rud" is a place name ending, and mainly in Norway, plus some parts of west Sweden. It's a more plausible name for later history when commoners started taking their farm names as family names.

Anyway, so Grabbe definitely existed and was rewarded for his valor against the Danes, raising his status from probably having been kihlakunnantuomari of east Raseborg to becoming the vouti of that province and later Viipuri. He must have done something right, and he must've been up to something between the failed siege of Turku castle and the successful one. On the other hand, Peder Svart's account of him is only a paragraph or two in total and there's every reason to think he'd exaggerate stories about daring raids against the Danes. But on the other hand again, one might wonder how Grabbe seized the flotsam and jetsam which he deposited in Tallinn in the middle of the war.

(DF = Diplomatarium Fennicum)