1) Definitely Aiptasia and you need to get rid of it ASAP. I prefer Aiptasia-X, everyone has their own preference. Since it's on a rock by itself, you may want to try just boiling some water, putting it in a syringe and shooting it right at it. Whatever you do, no not try to just pluck it off.
2) Looks like a Majano, (better pic would help) equally as bad. Again, the same method for above will get rid of it. They are a little hardier and it may take more than one application.
Peppermint shrimp are 50/50. Purchase a bottle of Aiptasia-X and keep it on hand. I've had the little bottle for over a year and even with a huge majano outbreak, it's lasted. You don't need that much to kill them, a little dab will do it.