tamed animals cannot starve to death in valheim. but if not feed theyll stop breeding till you feed them again.

other dangers include raids and all hostile creatures that get too close to the tamed creatures.

all tames are very vulnarble to flyers. the bat raid will kill all your tames if you dont hold them in a enclosed shelter with a roof as most tames are helpless againist bats.

boars will flee from fire. so dont have open fire near them.

chickens need a fire to hatch but are prone to self immolation so make sure they cannot reach the fire (hanging braziers work great for this or haveing a fire next room behind a wall)

wolves will fight and can be told to guard an area.
lox can be mounted if you add a saddle to them.
wolves can be told to follow the player once tamed. not possible with any other tame. so keep that in mind when tameing something somewhere.
you can enable friendly fire and use the harpoon to drag tames around. be wary of thier hp tough.
tames regen hp over time when they are feed.

no tame needs open sky. unlike crops.
eggs need a heatsource to hatch in range of them. otherwise theyll stay on the floor for good till picked up.