They do, however, there does seem to be some sort of reduction in the effectiveness of vampiric effects when triggered by area-effect spells. The exact amount varies, but this is easy to verify in game if you switch between a single target and area spell.
They do indeed. The best way to see this working is to turn on "Show Healing" in the options menu and perform the AoE skills. Unfortunately I can't get you a screenshot of this right now, but hope this helps!