Trainers » Green's Exploration | Trainers » Sabrina's Suggestion
Can I use Sabrina's Suggestion to copy an opponent's Green's Exploration in their hand if I have a Pokemon in play with Abilities?
Nope sorry, you still have to obey the restrictions on the copied Trainer card. Since you have a Pokemon with Abilities in play you cannot use Green's Exploration even from your opponent's hand.
Source: TPCi Rules Team (2019-09-12)
Trainers » Green's Exploration | Trainers » Power Plant
If I have Pokemon GX with Abilities in play and the Power Plant Stadium is also play, can I now play Green's Exploration since those Pokemon "have no Abilities"?
Yes, you would be able to play Green's Exploration in that case.
Source: Unbroken Bonds FAQ (2019-04-19), TPCi Rules Team (2019-05-02)