If I attach a Basic Energy to Eevee and trigger its "Energy Evolution" ability but choose an evolution belonging to Team Plasma, would I take the damage from Frozen City stadium or not?
The mandatory effect of the Frozen City stadium comes before the optional effect of Energy Evolution. If the Eevee is not a Team Plasma Pokemon before choosing whether to use Energy Evolution, you would take the damage from Frozen City.
Source: TPCi Rules Team (2014-08-28)
If I have more than one Machamp in play, do I get +20 damage for each one of them?
Yes, but only for each one that has the "Fighting Fury" Ability.
Source: Furious Fists FAQ (2014-08-28), TPCi Rules Team (2014-08-28)
Is Klefki's "Secret Key" ability stackable? Can you increase Resistance by -40 for each of them?
No, regardless of how many Klefki you have in play you only get a maximum Resistance of -40 from Secret Key.
Source: Furious Fists FAQ (2014-08-28), TPCi Rules Team (2014-08-28)
If I use Dusknoir's "Sinister Hand" Ability to KO my opponent's Active Pokemon, can I wait until my opponent replaces his or her Active Pokemon before taking my prize(s)?
No, per the rulebook you must take your prizes first, and then the opponent replaces his or her Active Pokemon.
Source: TPCi Rules Team (2014-08-28)
For Eevee, can you attach an energy and use its "Energy Evolution" ability and evolve on your first turn? How about on Eevee's first turn in play?
Yes. You can evolve on your first turn and also on the turn that you played Eevee via this Ability.
Source: Furious Fists FAQ (2014-08-28), TPCi Rules Team (2014-08-28)
Can I use Evosoda on a Caterpie the first turn of the game or the turn that Caterpie is played since "Adaptive Evolution" says it can evolve in those cases?
No, you can't use Evosoda to evolve in either of those conditions because the text on Evosoda specifically prevents it.
Source: TPCi Rules Team (2014-05-29)
Emolga with a Grass energy attached is poisoned and uses its "Call For Family" attack to get Virizion EX with "Verdant Wind" ability. Does it take poison damage or not?
No, because Virizion EX is in play before the end of the turn and Poison damage is taken between turns.
Source: TPCi Rules Team (2014-01-02), TPCi Rules Team (2014-05-08)
Can I use Caterpie's "Adaptive Evolution" Ability to evolve into Metapod, then immediately use Metapod's "Adaptive Evolution" Ability to evolve into Butterfree all on the same turn?
Yes, you can.
Source: Flashfire FAQ (2014-05-08), TPCi Rules Team (2014-05-08)
Does Drifblim's "Drifting Balloon" Ability affect the attacks from the Drifloon beneath it when Celebi EX with "Time Recall" is in play?
Yes, the attacks used from Drifloon will cost one less energy for each of the opponent's Team Plasma Pokemon in play.
Source: TPCi Rules Team (2014-05-08)