Can you play Darkrai GX with "Restoration" Ability from your Discard Pile if Power Plant is in play? And if so, do you do all of its effects?
Since the Discard Pile is not considered "in play", Darkrai GX can use its Restoration Ability to put it onto the Bench and attach a Darkness Energy card from the Discard Pile to it. Once all of the Ability's effects are complete, then Power Plant shuts off the Ability.
Source: TPCi Rules Team (2019-06-06)
If I use Darkrai GX's "Restoration" Ability and then somehow it gets back into the Discard Pile (e.g. Parallel City, followed by Field Blower), could I use "Restoration" again to retrieve it from the Discard Pile?
Yes, whenever Darkrai GX is in the Discard Pile, you may use Restoration during your turn as long as its Ability has not been disabled.
Source: TPCi Rules Team (2017-08-31)
If I have Darkrai-GX in my discard pile but no Darkness Energy, can I use its "Restoration" Ability?
Yes, Restoration only requires that Darkrai-GX is in the discard pile (and that you have space on your Bench for it).
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)