You can technically treat the animals badly but thats a player choice, some scenarios show animals in bad living conditions but you're sent to fix them.
Nothing explicit is shown, just too small enclosures and inappropriate enclosure set up.
Many animals including wolves and hyenas can fight for alpha status, causing injuries. The animals can be seen and heard fighting, and there will be a notification for it. The player can prevent this by limiting the amount of males in a habitat.
There are mutliple species of spiders you can choose to keep as an exhibit animal. This is optional, however their icons will appear on the zoopedia and exhibit animal trading menus
Animal deaths are not gorey in any way, it looks as if they're sleeping. Carnivorous animals will eat meat and carcasses brought in by keepers, but it isn't overly detailed
Spoiler for story mode!! For a while it is believed that a parent of one of the characters in the story is dead, they turn out to be alive, tho. It is only mentioned through dialog.
Animals can become injured (either from being a rescue, or fighting with other animals) but its not bloody and its rather cartoony.
If you wanted battles to the death and lions eating guests Jurassic World Evolution style, thats not what happens in this game.
Animals wont fight to the death, and if a dangerous animal escapes they will just run around and scare the guests.