If my opponent uses Guzzlord's "Red Banquet" attack and my Active Pokemon with Big Parasol attached gets KO'd, does my opponent get to take an extra prize for "Red Banquet" or not?
Big Parasol prevents all effects of attacks from your opponent's Pokemon done to your Pokemon; but taking an extra prize is a game effect, not "an effect done to your Pokemon", so your opponent gets to take the extra prize.
What happens if both Corviknight VMAX with "Lustrous Body" and Galarian Weezing with "Neutralizing Gas" are in play? Do they cancel each other out or what?
Lustrous Body takes precedence over Neutralizing Gas. It doesn't matter which one comes into play first.
Say Team Magma's Secret Base and Mimikyu with "Shadow Box" Ability are both in play. If I put Dedenne GX on the Bench, can I use its "Dedechange" Ability or will it be blocked because it has damage counters on it?
Since Dedechange and Team Magma's Secret Base are simultaneous effects, it is up to the player to choose the order in which they will be applied.
If my opponent takes a prize and then I use Naganadel GX's "Injection GX" attack to add a prize to my opponent's Prize Cards, would my Dubwool V's "Revenge Blast" attack do only 120 damage because the number of prizes in my opponent's Prize Card area has increased? Or does it do 150 damage (120+30) because the opponent has already taken that prize (even though it is now back in the prize pile)?
Revenge Blast is based on the number of prize cards TAKEN, so even though the Prize Card gets put back into the opponent's area it still counts as +30 damage for Revenge Blast.
Can I use Houndoom's "Single Strike Roar" Ability if all four Single Strike Energy cards are in play or in the discard pile?
No you cannot. Since the location of all four Single Strike Energy cards are known, there's no way Single Strike Roar would be able to find one during a deck search.
You can have four Single Strike Urshifu V and four Rapid Strike Urshifu V in your deck because "Single Strike" and "Rapid Strike" are part of the card name for these cards. Also, Single Strike Urshifu VMAX must evolve from Single Strike Urshifu V (and vice versa for the Rapid Strike ones).
Source:
Battle Styles FAQ; TPCi Rules Team (2021-03-18)
When I play Cheryl, can I choose not to heal one of my Pokemon that only has a few damage counters on it so I can avoid discarding the Energy attached to it?
No, there is no choice. All of your Evolution Pokemon that have any damage counters on them will be healed and have to discard their energy when you play Cheryl.
Source:
Battle Styles FAQ; TPCi Rules Team (2021-03-18)