#1 = Caulerpa racemosa peltata - It's a good algae for an algae scrubber or for Rabbitfish food. I would not recommend it for a display tank because of the spped at which it grows. It will send runners through coral flesh and damage coral. If you want to trim it everyday then I suppose it could be kept in a display tank.
#2 - I don't know, need a better picture. As a wild guess I'd say some form of Codium.