From left to right and in the row they appear to be in:
Toadstool, toadstool, (looks like) frilly mushrooms, anemone
red/purple mushrooms, Candycane coral,
Box is covering this coral, Suncoral, Don't see anything near the box, but im' assuming you're pointing to the zoanthids or paly
You can keep all these corals safely, with the acception to the Candycane you may need more lighting then this. Soft corals are going to be your best bet such as, Kenya tree's, cauliflower coral, Devils hand leather, xenia and greens star polyps. there are more, but i can't remember them... it's too early.