The game is about fighting monsters. Palicos and Palamutes can be hurt by monsters. They do not bleed, just flinch or are blown away. If the player hits a Palico or Palamute, they flinch but do not take damage.
There are dog like companions that you can hire called Palamutes that will help you fight monsters. There are also monsters inspired by dogs and canines, such as Zinogre and Lunagaron. There's no dog fighting like in real life, though.
They can be placed to fight on the frontlines against monsters, but the game treats it as normal. You can interpret them being there willfully and never being in danger.
Upon hitting a monster with an attack, there is a flash of blood. Monster parts can be broken and some have severable tails. You can turn off blood in the options menu.
You can eat bunny dango in the game which gives boosts to hunting. There are some chewing noises, but it did not bother me specifically. There's a monster called Chameleos that will whip its tongue around which makes wet sounds that trigger my misophonia. Some other monsters will make wet noises too.
In the cutscene before the Amatsu fight there is a still image of one of the characters as a baby. This is the only depicted human baby in the entire franchise to my knowledge.
There are story cutscenes in which a couple characters can commune with monsters. They don't really act possessed or hurt anyone, the monster just speaks through them.
The monster Volvidon has an attack that is basically just a fart which inflicts the dung status effect. There are many monsters that attack by spitting poison or fire.