Do things like plants, stones, deposits, animals respawn?

Mostly yes, If you don't change the ground around them with the terrain manipulator, they will come back. Even things like subterranean relics will respawn. (A useful early base location is near a cave with lots of relics.)

Deposits don't that I've seen. I think there's a certain number of terrain edits the game keeps track of, but it'd require making quite a few before the oldest revert. Even then, it might try to keep those done near a player's structure or might not restore the deposit.

I think its 2 game days before respawn