Can you use Mawile GX's "Captivating Wink" Ability if your opponent's Bench is full?
No. It's public knowledge that you can't put down any additional Basic Pokemon on your opponent's Bench, so you cannot use the Ability.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)
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)
If I evolve my Shroomish into Breloom (which has the Spore attack), can I use Amoonguss's "Bursting Spores" Ability?
Yes, because you have played a Pokemon that has the Spore attack from your hand during your turn.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)
Does Heatran GX's "Burning Road" Ability work if it becomes your Active Pokemon as a result of an attack like Archeops' "U-turn"?
As long as Heatran GX becomes your Active Pokemon during YOUR turn, it can use Burning Road.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)
If I have Focus Sash attached to Marshadow & Machamp GX and then use its "Acme of Heroism GX" attack, which one takes precedence if Marshadow & Machamp GX would be KO'd by damage from an opponent's attack?
You would choose, as they have the same effect, you choose the order of resolution.
Source: TPCi Rules Team (2019-06-27)
If Reshiram & Charizard GX has the extra 3 Fire Energy for "Double Blaze GX's" bonus effect and attacks a Whimsicott GX with "Fluffy Cotton" Ability, does the Whimsicott GX get to flip for "Fluffy Cotton" or does the "Double Blaze GX" attack go through automatically?
Technically speaking you still flip for Fluffy Cotton, but regardless of the flip's outcome the Double Blaze GX attack ignores the effect and does the damage anyway.
Source: TPCi Rules Team (2019-06-27)
If I use Raichu's "Evoshock" Ability to paralyze my opponent's Active Pokemon, does the Paralyzed status condition get removed if my opponent attaches a Stealthy Hood to that Pokemon on their next turn?
The Evoshock Ability's effect is to Paralyze the opponent's Pokemon; once that Special Condition has been placed it is no longer considered an effect of the Ability at the time your opponent attaches the Stealthy Hood. Therefore, your opponent's Pokemon remains Paralyzed.
Source: TPCi Rules Team (2019-06-06)
If I have Porygon-Z with "Crazy Code", but my opponent has Honchkrow GX with "Ruler of the Night" active, which Ability takes precedence?
Even though you're using an Ability to attach the Special Energy card, Honchkrow GX's Ability prevents you from playing it from your hand.
Source: TPCi Rules Team (2019-06-06)
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)
My Active Pokemon got Knocked Out between turns because it was poisoned and Weezing now becomes the Active Pokemon; does its "Detention Gas" Ability work?
No, because you wouldn't replace your KO'd Pokemon until the between turn phase is over. When Weezing comes up, it's too late for Detention Gas at that time.
Source: TPCi Rules Team (2019-06-06)