Quick question for clarification. I know the cc of a face down card is zero when it is in play. Is it also zero while on the stack, or is it like chalice (or other x spell) where it has a cost on the stack but not in play?
The cost on the stack is also zero, which is why draining it nets you zero mana.
The converted mana cost is determined by the mana cost in the upper right corner of the card.
Face-down creature spells and permanents do not have a mana cost in the upper right corner, so it is defined as being zero.