Much better pictures!!
The second are clove polyps, and the first ones are mushrooms and palys, like others have said. Those are really pretty mushrooms, btw.
I actually wouldn't try to thin out or kill the mushrooms. Those red mushrooms are much more valuable than the zoanthids on that rock. Red ones like that sell for $10+ EACH at my LFS. And they make the tank look so much fuller and nicer.
Palythoas are just plain old brown button polyps and are cheap and kind boring looking (IMO).
I would leave the mushrooms, hope that the palys can come back, but if they don't, no sweat. But the mushrooms you do have are of a sought after and expensive color morph, so if you got those as hitch hikers, you lucked out royally, as anyone buying that rock in my LFS would likely pay at least $100 just for the mushrooms in the portion of the picture you posted.