Ooo, good questions.
1) Yes, use tall/short for animals, high or low makes me think of relative placing eg "the snake is higher than the ant" I would assume means the snake is on higher ground (or in a tree) than the ant.
2) I have a tall fence at the bottom of my garden but you are right, I would rarely say "a high tree", again, my instinctive reaction to that is that it refers to a relative placing eg it's higher up the mountain than the other tree.
3) I need to think about this one! I'm struggling to think of an example of when I would say "a high building" but it doesn't sound wrong to my ear.
Great questions, really making me think!