If I use Rabsca's "Revival Blessing" attack to put Charizard ex onto my Bench, can I use the "Infernal Reign" Ability to search for and attach up to 3 Basic {R} energy?
No you cannot, because Charizard ex is not being played from your hand to evolve 1 of your Pokemon.
If my opponent has an Abomasnow with "Freezing Disaster" Ability in play, can I use Munkidori's "Adrena-Brain" Ability to move damage counters off one of my Pokemon or would that count as "healing"?
Yes, you can do that. Moving damage counters off a Pokemon is not the same as healing damage (similar as to how moving damage counters onto a Pokemon is not the same as doing damage to it).
Can you use Iron Leaves ex's "Rapid Vernier" Ability while Klefki's "Mischievous Lock" Ability is active?
No, you cannot. Rapid Vernier does not activate until Iron Leaves ex is on the Bench, at which time it is considered "in play" and therefore blocked by Mischievous Lock.
If Radiant Jirachi with the "Entrusted Wishes" Ability is KO'd by Quaquaval ex's "Exciting Dance" attack which pushes it to the Bench after doing damage, do you still get to search your deck for up to 3 cards or not since Radiant Jirachi is on the bench by the time KO's are checked?
Yes. Entrusted Wishes checks for two things here: Radiant Jirachi was damaged by an attack while it was your Active Pokemon, and Radiant Jirachi was Knocked Out by that attack. So even though you don't check for a KO until the attack is completed, the criteria for using Entrusted Wishes has been met, so it can be used. This holds true for any similar Ability that triggers when the Pokemon is Active and gets damaged by an attack.
When I use Palafin's "Zero to Hero" Ability, do I shuffle both Palafin and the Basic Finizen cards into my deck, or just the Stage 1 Palafin card since it says to shuffle "this card" into the deck?
Only the Palafin goes back into the deck. Finizen stays in play, going underneath the Palafin ex.
Source:
Twilight Masquerade FAQ; TPCi Rules Team (2024-05-23)