If I have Florges with "Calming Aroma" in play my attacks cost one Fairy Energy less. So I think I can use Zygarde's "Core Enforcer" attack without a Fairy energy attached, but what about the part of the attack that says to discard one Dark and one Fairy energy from this Pokemon?
You do as much of the attack text as you can, which in your situation means simply discarding one Dark energy.
Source: TPCi Rules Team (2017-09-21)
Can I use Heavy Ball to search for Wimpod that has the "Wimp Out" Ability on my first turn?
Yes, you can. Abilities only work when in play (unless the card says otherwise), so Wimp Out is not active while Wimpod is still in the deck.
Source: TPCi Rules Team (2017-09-14)
Weavile's "Rule of Evil" attack does damage to each Pokemon that has an Ability. But if Garbodor's "Garbotoxin" Ability is activated would "Rule of Evil" only damage Garbodor?
That's right, because Garbotoxin says each Pokemon (except those with Garbotoxin) have no Abilities.
Source: TPCi Rules Team (2017-09-14)
If I use Guzma and choose my opponent's Primal Groudon-EX that has the "Omega Barrier" Ancient Trait, do I still get to switch my own Pokemon?
Since Omega Barrier prevents the first effect of Guzma, you do not get to switch your Pokemon.
Source: TPCi Rules Team (2017-08-31)
Can I play Guzma if my opponent doesn't have any Pokemon on their Bench?
No, you cannot. If the opponent doesn't have a bench there's no way to do the second part of the trainer, and you cannot play a Trainer card for no effect.
Source: TPCi Rules Team (2017-08-31)
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 play "Guzma", who chooses which Pokemon to switch for each player?
You make all of those choices.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
Can you play Captivating Poke Puff 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 play the card.
Source: TPCi Rules Team (2016-08-11), TPCi Rules Team (2017-08-03)
If my opponent has no Benched Pokemon, can I still use Alolan Muk-GX's "Tri Hazard-GX" attack?
You can use it, but it won't have any effect, and it will count as having used your GX attack for the game.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
If I use Bruxish's "Synchronoise" attack against my opponent's dual type Pokemon like Volcanion EX, and there are other Volcanion EX on the Bench, do they take 40 damage or 20?
They take 20 damage.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)