You can either take out the molt or not. Some people get grossed out to see it in there, but in you leave it the CUC will eat it eventually. It depends in if it bothers you or not.
Cleaner shrimp IMO
do need to be fed a little. They'll kinda pick at rocks and eat any food that has gotten stuck in the rock, but my cleaner shrimp goes nuts for frozen food like bloodworms, mysis, etc. all of his little hands go crazy trying to catch it and shove it in his mouth. It's pretty cute to watch.