"It's What My Character Would Do" - The DnD Excuse That Ruins Games 

The dungeon master: An innocent child walks up to you… Me: I cast thunder spell!

Communication is key. Every RPG table should have a Taboo list. Simply a list of things that will not happen in the game no matter what. This is typically something you discuss during session Zero. My table's current list is: No rape, no racism, no animal cruelty. As for "This is what my character would do": This is the mind set you should have at all times when playing the game, it is a role playing game after all. BUT, it needs to be tempered by what is ok at the table and how it effects the other players (and DM) around it. In other words once you have thought through "what my character would do", you're not done, you then need to consider "will this ruin the experience for the others?", if the answer is "no", then carry on. If the answer is "yes", then you need to rethink what your character's course.of action.

I once made a character who was about 40% inspired by Batman, and about 30% inspired by Moon Knight, and one of the other PCs was an infamous martial arts assassin. I feel like some folks at the table were expecting me to go all punch-punch-punch on her when our PCs met, but my character essentially put her on his payroll, figuring she’d do a lot less killing on his dime than if he let her continue to work freelance.

The simple solution to the a player stating "It's what my character would do" is a very simple question to that player. "Why did you create a character that would do that in a co-operative game?"

"It's what my character would do." -> "You wrote the character and your choices are disruptive. Your character is not more important than the people you're playing with. Your personal enjoyment is not worth other people's misery. Blaming _your choices_ on the character _you wrote_ is a cop out. If you continue to behave this way, we simply won't invite you back to play with us." Bam, solved. Nobody's participation in your game is worth everyone else's fun.

It depends on the group, really. Which is why communication and sessions 0 are so important. Some people are ok with uncomfortable scenarios and some aren't. If everyone at the table is ok with being a murderous psychopath and want to immolate every man woman and child they come across then go ahead and do that. As long as everyone's having fun then there shouldn't be an issue. By that same token, everyone at the table should respect a person not being comfortable with a certain scenario.

the "glossing over" is usually what we do when a player doesn't care for a part of the story. when any plater says: "can we skip that?" if that is important to the story, we say something like: "what is the goal of the interaction?" then roll some dice to decide if it was successful. be it eating grape, ending an animals life, bullying, willing love making, long small talk or any other thing that someone may find less engaging. i once played a character that the other players loved, but their characters HATED him so much that on session 23, they killed him in a really horrible way. and i was all for it, i was even shocked that it took them so long to do so. as long as the other players are for it, all is permitted. but "trigger warnings" may ruin the surprise of the game. when ever you notice something you don't like, skip it.