If Cinccino uses "Amazing Plea" and there are zero cards in the discard pile, do I automatically do 80 damage? Or what if I only have one card in the discard pile?
The answer is the same regardless of the number of cards in the discard pile. Your opponent decides whether you take the cards (even if it's 0) or do 80 damage.
Source:
Crimson Invasion FAQ (2017-10-20), TPCi Rules Team (2017-11-02)
When using Mamoswine's "Forceful Tackle" attack, can I put enough damage counters on Mamoswine to knock it out? In other words, can I put more damage counters on it than it has HP remaining?
Yes, you can put up to 9 damage counters on it even if it doesn't have that much HP remaining. The extra damage will be done, and at the end of the attack Mamoswine will be knocked out.
Source:
Crimson Invasion FAQ (2017-10-20), TPCi Rules Team (2017-11-02)
Gourgeist's "Pumpkin Bomb" attack says to "discard any number of Pokemon Tool cards from your Pokemon", but can I choose a different Pokemon other than Gourgeist for this attack?
The term "Pokemon" in the attack is plural, so you can choose any or all of your Pokemon and discard as many Tool cards as you like from them.
Source:
Crimson Invasion FAQ (2017-10-20), TPCi Rules Team (2017-11-02)
In a single-elimination match that goes to time and is tied during the final game, if I add prizes to my opponent's field with Nihilego GX's "Symbiont GX" attack on my turn, do I win?
Yes. After regulation time (plus any additional turns) is completed, once you have fewer prizes remaining than your opponent, you win.
In a Sudden Death game, if I add prizes to my opponent's field with Nihilego GX's "Symbiont GX" attack, is the game won by the next player to take a prize, or the first player to take their last prize?
A Sudden Death match is complete when a player has taken all of their prizes, regardless of whether there is more than one or not. So adding prizes in this scenario makes it more difficult for the opponent to win.
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.
If I have a Dark Energy, a Rainbow Energy, and a non-Fairy energy card attached to Zygarde, when I use Zygarde's "Core Enforcer" attack can I discard the Rainbow Energy first for the Darkness discard, and then without a Fairy energy attached I'm done?
No, since you have Rainbow satisfying the Fairy Energy condition you would have to discard both the Rainbow and the Dark Energy.
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.