Can someone tell me, do I need to cover the foamcore board or can the cake be placed directly on it? I've heard both...

Depends on what you need it for. I use it for stacked cakes and dont cover. If using for a base then cover it. I use freezer paper for the white, then I have silver & gold foil paper.

If its for the base, you can use Royal Icing, Fondant, Foil paper.