I feed my corals, as they do much better when being fed IMO.
They wouldn't devote a majority of their surface area to feeding apparatus if they didn't need to. Nevermind IME once they are healthy and your water quality is good - I've gotten better results [colorwise] when feeding them.
As for what, leftovers from the fish, small meaty foods, and whatever else I throw in my mush [Cyclops-eeze, rotifers, etc], detritus, bacteria ...