Balrogs are Maiar, but they have also assumed a physical form, so that form probably does eat. Balrogs eat anything they want (Dwarves, nameless things in the depths of the earth, etc.)! The Balrog of Moria also seems capable of entering long cycles of hibernation.
Well Balrogs are Maiar so they do not need to eat, and if they do it's probably same what have other servants of Darkness. About entertainment they're creatures of Violence so they entertain by causing pain to others, torturing enemies of Melkor as it is described in Unfinished Tales.