I don't know the show, but I do know a bit about Vikings in North America. We've got the two "Vinland Sagas" about them, and these are somewhat fictional stories written a long time later in a different place, so kind of like watching Western movies from Hollywood to figure out what the old west looked like. And we've also excavated a long-term camp (not a permanent settlement) they set up at a place called L'Anse aux Meadows in Canada. Without researching the show itself then, I can at least respond to the questions you've posed about Thorfinn.

Regarding Vikings and Danes, it's important to note that Viking is a modern term that groups people together who might never have thought of themselves as belonging to a single group. The guys (and maybe gals) who came to Vinland had traveled from a small population of folks—maybe 4000?—who had settled on Greenland, and they were sort of a fringe population of the 40,000 or so folks in Iceland. The folks in Iceland saw themselves as most closely related to people who lived in Norway, though they were proud of their migrant status, much as early Americans were proud of having left England and fought the American Revolution. Denmark, of course, was even further afield, so asking how a Vinlander like Thorfinn could hate Danish Vikings is something like asking how America could fight WWII against the Germans, since they're both Western countries. Put simply, the term Viking is so ridiculously broad that it masks more than it reveals.

Viking orgies? No evidence. Which isn't to say they didn't happen, but outsiders who visited Scandinavia and wrote about their experiences didn't see it as a pervasive public problem, and it's the kind of thing that bishops like Rimbert or devout Muslims like Ibn Fadlan would likely have mentioned. Ibn Fadlan does admittedly talk about Norse-speaking slave dealers raping their slaves in front of each other, but there's no reason to assume this behavior was representative of the broader Viking diaspora, and I'm not sure that qualifies as an orgy anyway.

Cottages with severed heads? I'd say there's evidence to the contrary, insofar as archaeologists have dug up hundreds of Viking Age sites and not found heads on poles. It does seem that human heads were sometimes mounted on the walls of Dublin, but this is probably best understood as evidence that the Dublin Vikings adopted to the legal norms of the British Isles, where judicial beheadings and bad burials were pretty common in the late Viking Age on either side of the year 1000. There's also a pretty amazing farm at Hofstaðir in Iceland where they mounted cow heads, suggesting that the farm was a sort of religious site and they displayed memorials of their ritual feasts, but then again, cows aren't people.

Fish? That's probably right. The Vinlanders were really just visitors from Greenland, and the folks in Greenland successfully adapted to live in the far north for about 500 years before their settlements disappeared around 1450 or so. They certainly liked walrus and seal, in part because the big land animals they were used to, like sheep and cattle. We know that people in Iceland were very excited when they found places where they could expect annual salmon runs. And we also know that people in the North Atlantic started doing more deep see fishing for things like cod around the year 1000. So fish would probably have been a staple and maybe even a delicacy for this Thorfinn character.

Incidentally, I'd suspect that your character Thorfinn is named after Thorfinn Karlsefni, who has his own Wikipedia page. It is, like many Wikipedia pages I've seen on saga characters, a strange mix of positivism (what the sagas say must be true!) and prejudice (my saga is more truthful than your saga!). But it can give you the quick and dirty to see if he's someone you want to read more about. If so, I'd strongly recommend picking up a copy of the Vinland Sagas, which is really a pair of short stories with a good introduction. With a bit of effort, you might consider it a good weekend read.

Sounds like a good show!