If I use Seedot's "Harden" attack which prevents any attack damage that is 40 or less during the opponent's next turn, does that come before or after calculating for Weakness/Resistance?
Weakness & Resistance are factored in before determining whether Harden blocks it or not. So if a fire Pokemon's attack does 30 damage to Seedot and then +30 more is added for Seedot's Weakness, Harden would not prevent the damage. However, if the fire Pokemon's attack does 20 damage to Seedot and then +20 more is added for Seedot's Weakness, Harden would prevent the damage.
Source:
Celestial Storm FAQ (2018-07-20), TPCi Rules Team (2018-08-02)
What happens if I try to use Volbeat's "Pheromone Catch" attack, but Illumise was KO'd during my opponent's previous turn?
Volbeat's Pheromone Catch is a game state check; it doesn't matter if Illumise is even in play anymore. As long as one of your Illumise used Pheromone Signals during your previous turn, you get the bonus when using Pheromone Catch.
Source:
Celestial Storm FAQ (2018-07-20), TPCi Rules Team (2018-08-02)
For Weavile's "Evil Admonition" attack, can I count Pokemon in the discard pile with Abilities too, or just the Pokemon in play on the field?
In this case the phrase "your opponent's Pokemon" refers to the Pokemon in play on the field, not to your opponent's Pokemon cards in the discard pile or elsewhere. Generally when referring to "your opponent's Pokemon" it means in play unless another specific game zone (like the Discard Pile) is mentioned; if they don't specify a zone, then "in play" is assumed.
Does Mewtwo's "Pressure" Ability block all of Tapu Koko's "Flying Flip" Attack's damage, even to the bench?
Pressure says, "your opponent's Active Pokemon's attacks do 20 less damage." Since it does not specifically designate Active or Benched Pokemon it reduces damage by -20 to each Pokemon that would be damaged by the attack.
If I use Guzzlord GX's "Eat Sloppily" attack and discard a Beast Energy {*} card, would it get attached to the Guzzlord GX, or would it go straight to the Lost Zone because it was discarded?
When "discarding the top 5 cards of your deck", any revealed Energy cards get attached to Guzzlord GX immediately, before they reach the Discard Pile. Therefore, Beast Energy {*} gets attached to Guzzlord GX rather than going to the Discard Pile or Lost Zone.
If Lysandre Labs is in play and I use Primal Groudon's "Gaia Volcano" attack to discard the stadium and do enough damage for KO, what happens if the full HP Fighting-type Defending Pokemon has Focus Sash attached to it?
While Lysandre Labs is in play Focus Sash has no effect. However, Lysandre Labs is discarded as part of the attack before KO's are checked. So the Focus Sash would be in effect and if all of its conditions are met the Defending Pokemon is not KO'd but has 10HP remaining.