What happens if M Gengar EX uses its "Phantom Gate" attack to copy Xerneas EX's "X Blast" attack? Can it use "Phantom Gate" again the following turn at all or not? Or would it just not be able to copy "X Blast" twice in a row?
The X Blast attack puts an effect on Gengar that prohibits using that particular attack next turn. But M Gengar EX is using its Phantom Gate attack on the following turn, so yes it is able to copy X Blast twice in a row.
Source: TPCi Rules Team (2015-01-22)
Does Mega Gengar EX have to have the correct types of Energy attached to it to do an attack that is copied by "Phantom Gate"?
No, it just needs the Energy required by Phantom Gate.
Source: Phantom Forces FAQ (2014-11-13), TPCi Rules Team (2014-11-13)