Ya, they eat everything. I have 8 or so in my tank, and didn't have aptasia to begin with. Just overall good cleaners, eat left over food, etc.

Oddly, peppermints usually being very secretive, mine are out all the time, can't trim corals without them climbing all over my hands.

Yes they will eat the dead skin off your hands as well.
I had a cleaner shrimp, very mature, big one. I put my hand in the tank one time with a big scab from a cut, maybe a week or more old on the back of the hand. The cleaner went on my hand as usual, picking away, then found the scab. I was just glancing at him when I saw him hunker down with all legs while having ahold of the scab. He gave a huge push and he separated the scab off.
So surprised, and hurt, I whipped my hand out. Sure enough I was bleeding.
Bugger