Demon/extradimensional entity/alien thing, yes. It's never really explained what he is, he could even have been originally human (not anymore obviously.)
Given what we now know, I think he was originally human but altered by Willie and ingestion of Red Seeds.
The last boss fight and the ending implies he was a literal puppet animated by Willie.
Who names their singing bar "Galaxy of Terror?"
I think the answer to this is a neat piece of trivia. This game drops pop culture references like crazy as anyone who's played it knows, generally from the eighties and earlier. "Galaxy of Terror" is a cheesy, sleazy sci-fi/horror film produced by Roger Corman from the eighties, most notable for a scene in which a woman is raped by a giant space maggot, that scene being mentioned IN GAME. It also stars Sid Haig. SWERY knew all about it. It's a cult classic.
It has a S&M room in the basement. The name is, like, the least crazy part of the place.
George and Emily were both outside the lumber mill. How the Hell did George ditch Emily to attack York inside it?
That wasn't George, that was the previous Raincoat Killer, trapped in the Red World.
Alternatively, George slipped from the real world to the Other World, where he has Offscreen Teleportion powers.
Why did York never try and shoot the Raincoat Killer besides that one time?
He likely knew that wouldn't work. York obviously knows a lot more than he's letting on.
Why did Kaysen bother pretending to be friends with the Ingrams?
Maybe it wasn't exactly an act. Sure, he's a heartless bastard, but maybe he likes rock music, too. Or maybe he was scoping out Lilly for "soil." Or maybe he knew about the twins' powers, and was trying to figure out a way to repress that and/or take advantage of it.
Related: Why does Willie help Emily, leading her to the clock tower and saving her from Thomas? I can see Kaysen doing it to screw with her and York, but wouldn't Willie, being his handler (and thus theoretically the more practical one) give Kaysen an easy opportunity to off what would be the only remaining threat? (Unless Willie wanted Kaysen dead for his transgressions, of course...)
Presumably Kaysen was thinking ahead in terms of his "game" - he was likely already aware that York was going to be able to finish off George, and he wanted to ensure that both York and Emily would be around so he could get the most pleasure out of tormenting them in the final stage of his plans.
When Agent Morgan first encounters the Shadows, he's utterly nonplussed and all he has to say to Zach is "they're here, too." Where has he run into them before, and how long has this been happening?
Probably since his initial encounter with Kaysen.
Why do the Mysterious Shadows say "let me die," but then as soon as they're actually dead they come out with "don't want to die?"
Well, their card suggests they're victims of the previous slayings, possessed by demonic creatures. Just because they're aware death is better than the state they're in, it doesn't mean they like it.
So all of the goddesses of the forest except Emily were sexually involved with George right? Including the victims?
It's heavily implied, yes. Given the S&M basement and the description of the girls acting like "cats in heat" under the influence of the seeds, it also adds a creepy non-consensual angle to that...
What exactly do the red seeds do? It doesn't seem that simply ingesting them gives you superpowers, or the victims wouldn't have died and the whole ritual wouldn't serve any purpose. And what determines if it will grow into a red tree or not?
Based on how we see people behaving under their influence, and the effects of the purple gas on the town, the primary effect of the red seeds (on humans, anyway) is to cause insanity; superpowers/immortality might only happen upon ingesting a truly ridiculous amount, hence why George absolutely shovels them in during his boss fight. As for whether it grows into a tree, that seems to be based on whether Kaysen... fertilizes the ground or not.