The top pic is a Green Star Polyp. IME
Fairly easy to take care of. It will like light and encrust along your rocks.
The bottom pic is another story all together. It looks like an Alveopora. IME
can be difficult to care for. It neads moderate to high lights with moderate water flow. Ca
need to be well ballanced and it will not like any level spikes, so if you are dosing, make sure you do it slowly. Mine prefers the sandbed but it is supposed to like the middle to top area of the aquarium. I have read that the survival rate of these corals are very low in the aquaruim, but i have had mine for 3 months and so far so good. Good luck!