Yes, but she's a magical dog who fights via spellcasting, so it's pretty different from IRL dogfighting. Also she's sentient and completely willing to help with fights.
Yes, one of the main characters ends up fleeing the Dead on horseback and runs his horse too hard and she gets injured, and then he mercy kills her so the Dead don't kill her more cruelly. The horse wasn't a major character but she was named and given some characterization and her death scene is pretty upsetting for the main character and for me as a reader.
One of the main characters attempts suicide because she's upset that she doesn't have the same magical abilities as everyone else in her community. She gets interrupted and her life starts improving afterwards.
One of the main characters discovers she was conceived when her mother had sex with a man who had a daughter close to the mother's age. The sex is consensual but not motivated by attraction (there's a prophecy about the child they conceive) and the two seem pretty awkward about it.
Pretty sure some of the Dead Hands get finished off that way, but they're basically zombies. No living people or Greater Dead (the sentient kind of Dead) get crushed.
Not against any real-life culture, but some antagonists are described as saying hateful things about refugees from a culture that seems vaguely inspired by middle eastern people.
One of the main characters almost dies at the start of the story, and spends a bunch of the story struggling with symptoms remiscent of PTSD as a result.
One of the main characters gets held by the arm by the main villain, who tries and fails to implant a magical device that would let him control that character.
One of the main characters during a fight taking place between him and a major antagonist while they're visiting the afterlifeof that setting, which is a river.
A couple of the main characters spend awhile in hospital after getting attacked towards the start of the story. Later, another main character gets put in a hospital after getting injured fighting a monster.
One of the main characters was abandoned by her mother, who didn't say goodbye. The other has parents who are frequently busy with work, and while he's sick they have to leave before he recovers enough to know they're saying goodbye, and end up barely seeing him for most of the book.
Shadow Hands are intangible and undead so I think that counts. They don't really act very ghostly, though, more like zombies who don't have a physical body.