You can be by Cougars, but you can turn this off in the settings. This also happens in 'The Hunter's challenges and the 'Escape from the Darkwalker' challenge.
The death scenes are fairly quick, but in the story mode...
In the main game, unless your aim is bad you can kill in one shot. But the animal can bleed up for anywhere up to an hour in game.
((SPOILERS))
You need to repeatedly stab a bear with a spear in order to kill him, it takes a few rounds of him charging at you to finish him off.
You need to kill animals to survive, as well as the fact you can find prespawned corpses in some key locations for them include the Carter Hydro Dam and nearby the Trappers Cabin, otherwise, you can find them due to wolves chasing and killing animals.
One of the debuffs you can get is broken ribs, but it's easy to avoid if you don't provoke a moose. You can also sprain your wrist and ankles, but they heal within a few hours of rest.
Not necessarily torture, but there are (first-person POV) scenes of your character being injured/mauled by animals where you are helpless. In one of the challenge modes where you are hunted by a bear, a scene like this is unavoidable.
((Minor story mode spoilers)) In story mode, a 16-year-old is revealed to have died. This is mostly just implied in the main quest but is more explicitly the focus of a side quest you can do.
((SPOILERS))
In the story mode, there is a part where you are stuck in a train cart, a bear that is pursuing you then pops out of nowhere and knocks the car over.