The player can catch fish, and in fact has to do so on a couple of occasions for the game to progress. Presumably the fish die after being taken out of the water, but no attention is drawn to this fact other than some characters mentioning fishing for food.
Francis describes how she physically fought and hurt her friend, another dog - no visuals of it onscreen. Some dogs growl and bark at each other when they're angry, but they never come to blows.
On two occasions the player has to catch Ancient Fish in order to progress through the Kunka Ruins. The bodies of the fish can be seen on the pedestals after being placed there.
Bugs of all types appear in the game for the character to collect. Even if the player chooses not to collect them, they can always be seen in the open world and are thus unavoidable.
As well as the examples in the other comment, the player character can become unconscious if their health runs out from being attacked or staying too long in the desert/snow.
The player can bark at enemy animals to knock them out briefly.
The main character's younger sibling has an illness which can apparently be fatal. It is not stated to be cancer, though it could be interpreted that way. Another character's girlfriend is said to have also died of a mysterious illness. Once again, it is not stated whether the illness was cancer or not.