The second one is a frilly mushroom. Or hairy mushroom. I've got one but its just a frag. Yours is awesome. Can't wait till mine grows now. Have you tried target feeding it yet?
Are all the pics of the same coral? It looks like a forked corallimorph, we get ours from the caribbean. It's very similar to the frilly and hairy mushrooms, but the "tentacles" are forked hence the name.
Then mine is a forked corallimorph because it's identical to these pictures. Google fragoutpost.com it's a website for fragging info and there are forums for fragging these types of mushrooms.