The first one looks like hair algea, which is a problem algea. You could probably just rip it out with your hand. The second one is definitely aptasia, a problem anemone. It looks somewhat big from the pic so I don't know if a peppermint shrimp will eat it, they usually go for ones that are smaller than a few centimeters in diameter. If the rock can be pulled out easily you can do a quick dip in RO water or try and scrape it off with a knife (assuming it doesn't receded into a hole, which they sometimes do). A very successful way to get rid of it is by squirting boiling water at it, that will melt it away never to return.