Abilities » Captivating Wink | Attacks » Gigaton Shake
What happens if I use Steelix's "Gigaton Shake" attack, and then my opponent uses Mawile GX's "Captivating Wink" Ability during their turn? Would those Pokemon I put into play be able to attack on my next turn (since it was not during MY turn)?
No, they would not be able to attack.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)
Trainers » Channeler | Attacks » Gigaton Shake
If I used Steelix's "Gigaton Shake" on my previous turn, would Channeler allow my Pokemon to attack this turn?
Yes, the effect of Gigaton Shake would be removed, and your Pokemon would be able to attack.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)