If I kill my opponents 4/4 Primordial Hydra, will I be able to use my Cemetery Puca's activated ability on the Hydra, and have it become a 4/4 Primordial Hydra, or will my Puca die because the Hydra is considered a 0/0 creature when it is put into the graveyard, due to the X part of its mana cost?
So your Puca does have the "~ enters the battlefield with X counters", but that's irrelevant because it's not entering the battlefield anyway. The object already exists, it's just getting a facelift. (The X would be 0, but that doesn't matter because it isn't triggering.) As for the existing counters, the final clause states that counters are not copied. So you basically get to kill your own Puca by doing this. Which I suppose isn't so bad if you have a Blood Artist or something. =)