Coral Ids

I got some corals on some live rock I recently purchased.
The top one is, if I am not mistaken, an Open brain Coral. I am feed it chopped shrimp for now.
The other 2 in picture I am not sure of I think they might be closed brain corals of some kind.
The one on the left under the brain is a green color, the one on the right is gray, it unfortunately has a large dead area on it.
Any information on these three corals and their care would be greatly appreciated.
Thank you.
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Typically you don't have to feed brain, but it doesn't hurt.

The rest of things on that rock looks like sponges though. If they are soft, probably sponges. If hard, could be favia...maybe.
 
Found out that they are Lesser Starlet Corals.

I have feeding the brains around every 2 days and they are doing great the damaged brain coral is starting to inflate much more than it was.
Looks like I will have 3 brains; as I found another small one,or 4 if I decide to frag the damaged one.
 
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