I specifically don't feed any of my corals. I feed my fish, and they in turn feed the corals. However, you do have to supply proper alkalinity and calcium for any of the hard corals so they can build their skeletal structure.
As far as minimal tank size, I don't think there is one. In a very small tank you might need to trim back frequently, more or less a bonsai of monti.
I have both "plate" and "finger" monti in my tank, and the plate grows very fast. I trim mine back at least every six months.