no, the dog you play as in a later chapter cannot be harmed and is completely fine, BUT it should be noted that the first boss of the game is you literally exploding a cerberus-like dog that has dog howls and everything. you have to fight him twice (once in ch1 and a rematch in ch9), but he’s so cartoonishly evil it should be fine?
There are multiple instances in the game where Pit is injured to the point of unconsciousness on screen and Dark Pit mentions his own unconsciousness at one point
yes, if you consider a hydra-like creature dragon adjacent enough. you cut off its three heads, but it doesn’t regrow anymore. you do have to fight two of its severed heads and kill them, though, and rematch one of the heads later.
there’s also a few enemies with dragon-like appearances that you have to kill.
Some enemies are buglike, especially the ones in Chapters 11-14, with minor appearances of similar and previously mentioned enemies in later chapters. A main villain in chapter 20 and 21 is definitely a big creature, and disturbing at that. The levels it appears are also disturbing to a degree.
there are jokes about eating the main characters wings, two enemies turn you into food, with one trying to eat you, and a level that's spent inside the body of someone
An entire chapter features the protagonist possessing other people, as he was separated from his physical body. It's later revealed that this happened because a separate character got possessed and turned evil.
Many of the attacks, for example, mega-laser, can be used by the player, which has pulsing and flashing lights. The main attacks used by the player can also be particularly bright and flashing.
Chapter 11 involves basically a version that instead makes plants grow, but it still destroys a town. I recommend to be careful with this one, not sure if it qualifies.