Anton and especially Annie could be read as mentally ill and are extremely violent, though this is unconfirmed and could largely be a result of alcohol and caffeine abuse respectively. It's a (playable) cartoon so the characters' personalities are far from realistic.
Most characters' sexualities are not touched upon. There are only two canon relationships and they're both heterosexual. Satan is vaguely implied to be bisexual but he's implied to survive anyways.
Satan mocks the player with a "boo-hoo" and a mock crying face for presumably being sad that the game is almost over, but obviously the player's gender is irrelevant here.
Anton is obsessed with hard alcohol, to the extent that the goal of the game at large is to recollect his stolen spirits. This likely contributes to his rude and aggressive demeanor.
Sort of? Satan is dissatisfied with not being red enough after discovering there is someone redder than he is. Other than this, he seems quite proud of his appearance.
Religion isn't discussed in a philosophical way, but religious imagery frequently crops up, such as the obvious depictions of Hell/demons and a boss based on Biblically accurate angels.
Huge explosion that levels an entire city as well as presumably all of Hell. For what it's worth, all of the main characters apparently make it out unscathed.