They'll starve, unless you feed them starfish. Some people keep a chocolate chip starfish in their sump and cut off a leg now and then to feed the harlequin. They regrow their legs.
I'm not saying this is a good thing. Just repeating what I've read.
In my experience, asterina numbers flare up and diminish, depending on my tank conditions. I never worry about them.
Mine is ok with cleaner shrimps, can't say for blood shrimp, I don't have one.
Yes, they eat only starfish. I keep moving him from tank to tank, where ever the asterina population is the highest.