The protagonists’ inner monologue sometimes notices when a man has a vagina or a woman has a penis, but there is no disrespect. Trans characters, at least in this first book, don’t appear to be oppressed for their gender identity
Major spoiler major spoiler: a character has three names throughout the course of the book. She gets upset when an antagonist calls her by her child name. These names are not related to trans identity, but to defining different life stages
Not by the author. The book has people with races and abilities that do not have real world equivalents. There are people called orogenes who are consistently despised and oppressed throughout
The internal logic of the world in the book is consistent, if a bit difficult to piece together at first. It is very obviously not taking place on the same Earth where we live
Sort of. Children at the Fulcrum are taught that their punishments (some of which are quite severe) are fair and their bad emotional reactions to these things are the real problem. Schaffa, one of the Guardians, convinces his charges that he hurts them out of love.
This is kind of hard to answer, because all the characters are mixed race (often with racial features that don't align with our own races), and nearly all of them have dark skin. It would be more accurate to say many black people die all the time, but many also survive.
Major spoiler: Innon is murdered. Alabaster appears to die at one point, but it turns out he doesn’t die until the end of the book. Before the events of the book, Alabaster’s lover was killed by a Guardian
The more “unskilled” orogenes are if I remember correctly are given a lobotomy or something and kept captive in a vegetative state, basically comatose but not treated well