1. Aside from the obvious, like getting burned down or hacked apart? Guy's tough, but he' still in a tree. That's another thing; his physical body is in the tree, so if you can get past that and harm him, you pretty much kill him. But the same could be said of anyone wearing an unusual suit of armor. In terms of particular weaknesses, being able to manipulate plant life is, ironically, one of his weaknesses; while he has enough control of himself to move and act, there's little he can do against a druid, who could force him to do things against his will. And while he's not particularly weak against any element, he's not resistant to them either. I mean, getting lit on fire isn't any more lethal than doing it to a normal human, which is to say, still pretty bad.
2. No, he doesn't need Demonmancy to exist. He can't preform Demonmancy, but he's been to plenty of worlds where he can't do that already, so it's not something that he's unfamiliar with. The study of demons (Which is what we call Demonmancy) is important however, at least if he wants to find another Rift to leave this world. As I've mentioned they only appear in areas were there is a chaotic influence. Demons seem to be the most reliable source of this concentration, but other sources can be used if the effect is strong enough. General tips and tricks for figuring out if you're in a place where it could happen:
History of Evil magic, typically the type that involves sacrifices or dealing with evil entities.
Locations were lots of people died. Battlefields are often the usual candidate, though places like prisons and slave camps are more likely. Oddly enough not graveyards; most of the corpses there was died elsewhere. Though it can be a location for the above demon magic.
The Abyss and The Nine Hells are the most likely place to have a Rift, what with being demon worlds, but Karnage knows better than to jump headlong into those places without doing some serious study. Since he's very much aware of the large variety of demons and how they differ from world to world, he needs to figure out if he could be properly classified as a demon or not, or at least if he could survive entering The Abyss and The Nine Hells. Non-demons can't survive in the Inferno, and even regular demons have a hard time living there. Karnage knows he's not an exception. Not yet anyways.
That being said, while Karnage isn't capable of his original Demonmancy, he does have the potential for magic, being one of the few magic-capable orcs from both his native world, and hopefully this one. He just needs to figure out how magic works in this realm.
3. Karnage doesn't slaughter people indiscriminately... At least not here. He certainly had a past for it, as you might know. But that was in other realms, universes even. Here he has a clean slate, though he's still surly and will likely crush you if you anger him. But who wouldn't?
4. Don't worry, I don't plan for another Karnage to show up here. I just threw it out there in case you're wondering what would happen to the other Karnage if this one somehow ends up dead. Just so you know; this Karnage, while from the same world that you may know him from, is from a different continuity. Specifically the time between Act II and Act III. This is why he was dumb enough to just waltz right towards a mysterious portal in the Inferno; the current Karnage wouldn't do something so suicidally stupid.
5. Power wise he's a tanky-fighter type with some quirks that gives him abilities from other classes (Mostly plant talk and health regeneration, which isn't fast enough to be useful in combat), but not enough to make him seem like he's multiclassing. He has to learn magic all over again since he isn't sure how it operates here, so until he can find a teacher and sit down to study for the next twenty or so years to master it, his means of combat often involve getting to his target and ravaging it until it stops living. Normally he'd have some weapons to give him and edge, but because he's in a tree right now, his approach is simply just beating them to death, and using a mix of reaction time, natural durability, and experience to defend himself. Stat wise he's a
Might Glacier; slow and tough, but once he's in range he will end you. Unfortunately for him that range right now is only within arm's reach, but you can be damn sure that once you are, there's no escape. He might not be able to out run an energetic child, he can intercept a bird flying past him as long as he's aware that it's coming. That's due to living a good 400 or so years more-or-less getting into fights with everything that is capable of dying and than some. And he's not even as fast as he could be, which is due to being stuck in a completely unfamiliar body.
Sufficient to say, once he's freed (If he gets freed), it will be a major upgrade to his combat abilities.