Any feats I assign to regular Beast Boy can be used by characters (his other forms) he switches into, correct? And because you can assign any feat to any character, I could build a team with regular Beast Boy (in order to get a teen titans theme) and assign him Vampirism even though he doesn't have B/C/F?

Since all three of his other forms have at least 2 clicks of B/C/F, they would then be able to use Vampirism, correct?

You are correct on all accounts.

I'm going to go with yes on that one. I've read on here about other people doing the same as well and nobody has argued it that I have seen.

If you go to the Final Word for alter-egos his power works similar to that and it was ruled that they act as 1 figure.

yes, you can choose Beast Boy for Caeria and get the defense bonus on all versions as he chages (as long as he is next to her)

Oh wait, that wasn't the question? Looks like i answered the next one for ya

Another question regarding BeastBoy, can you hypersonic speed / attack with the cheetah and then switch into the T-rex. Or is HS w/ attack not conisidered a move action?

No, hypersonic speed is not a move action.