If I use Araquanid's "Bubble Net" attack and my opponent switches in a new Active Pokemon, can they attach an Energy to it during their turn?
Yes they can. The effect was on that specific Defending Pokemon and was removed when it went to the Bench.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
If I use Palossand's "Dust Storm" attack against a Stage 2 Pokemon, do I discard the Basic and Stage 1 cards attached to the Stage 2 Pokemon?
No. The Basic and Stage 1 as well as the Sandygast are part of their respective Pokemon and are not discarded.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
If I put a Charizard GX in play using Ho Oh GX's "Eternal Flame GX" attack, and my opponent evolves into Porygon-Z and uses its "Initialize" Ability, does Charizard GX go back into my hand?
No. Charizard GX is in play as an "unevolved Pokemon" and so is not affected by the Ability.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
If I use Ho-Oh GX's "Eternal Flame GX" attack, can I place a Stage 2 Pokemon like Charizard GX from my discard pile directly onto my Bench?
Yes. The attack does not specify that the selected Pokemon have to be Basic Pokemon.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
When using Drampa GX's "Berserk" attack, must ALL Benched Pokemon have at least 1 damage counter or do you only need 1 Benched Pokemon with a damage counter on it to add the +70 damage?
If any of your Benched Pokemon have damage counters it will add the +70 damage. If it required all of them it would have said "all" or "each" in the attack text.
Source: TPCi Rules Team (2017-07-06)
Does Umbreon GX's "Dark Call GX" attack have to discard 2 energy from a single Pokemon, or can I discard 1 energy from two separate Pokemon? Or does it mean to discard 2 energy from each of my opponent's Pokemon??
The term "Pokemon" in the attack is plural, but it doesn't mean all of your opponent's Pokemon. You may discard 2 energy from one Pokemon, or you may discard 1 energy each from two Pokemon.
Source: TPCi Rules Team (2017-01-26), TPCi Rules Team (2017-06-27)
Can I use Umbreon-GX's "Dark Call GX" attack to discard 2 Double Colorless Energy?
Yes, you can select 1 Energy of each Double Colorless Energy to discard both of them. This applies for discarding your own Energy for an attack and for retreating as well. So if you used Hoopa-EX's "Hyperspace Fury" attack or paid its Retreat Cost of 2, discarding 2 Double Colorless Energy would be legal options.
Source: TPCi Rules Team (2017-01-26), TPCi Rules Team (2017-06-27)
Say my opponent used Turtonator GX's "Shell Trap" attack last turn, then on my turn I attack it with Tapu Bulu GX's "Tapu Wilderness GX" attack. Does "Shell Trap" place its damage counters before or after the healing part of "Tapu Wilderness GX"?
Tapu Wilderness GX heals Tapu Bulu GX as part of its attack before the damage counters are placed for Shell Trap's effect. So in the end Tapu Bulu GX will have 8 damage counters on it.
Source: TPCi Rules Team (2017-06-08)
Say my opponent used Turtonator GX's "Shell Trap" attack last turn, then on my turn I attack it with Shaymin EX's "Sky Return" attack. What happens to the 8 damage counters effect from "Shell Trap"?
Sky Return puts Shaymin EX into the hand as part of its attack before the damage counters are placed for Shell Trap's effect.
Source: TPCi Rules Team (2017-06-08)