Can I play Eneporter to try and fail to move a Special Energy onto a Pyroar that is protected by its "Unnerve" Ability, or would I not be able to play Eneporter at all?
The fact that its effect will be blocked by another effect such as Unnerve does not prevent an Item or Supporter card from being played. For example, your opponent may play Eneporter to try moving a Special Energy and Pyroar is a valid target, but Unnerve blocks the effect even though Eneporter was played. Playing a card for no effect happens when the game state itself prevents any effect from taking place and in that case the card would not be played, but that is not what this example is referring to.
Source:
Forbidden Light FAQ (2018-04-20), TPCi Rules Team (2018-05-03)
The correct order for Milotic's "Energy Grace" Ability should be this: 1) Attach 3 basic Energy cards from your discard pile to 1 of your Pokemon (excluding Pokemon-EX), 2) Milotic is Knocked Out. That means you cannot use "Energy Grace" if you have no basic Energy in your discard pile, and you can't use "Energy Grace" to get back any Energy that are attached to Milotic.
If I use Sudowoodo's "Watch and Learn" attack on the turn after my opponent's Mew EX used its "Versatile" Ability, can "Watch and Learn" copy the attack that Mew EX used?
If I have multiple Infernapes in play, does each of their "Flaming Fighter" Abilities add 6 more damage to my opponent's burned Pokemon in between turns?
No, Infernape's Flaming Fighter ability does not stack. You are simply placing 6 damage counters instead of 2, regardless of how many Infernapes are in play.
Source:
Ultra Prism FAQ (2018-01-19), TPCi Rules Team (2018-02-01)
Can I use Lunala GX's "Psychic Transfer" Ability to move a {P} energy back to where I got it from on the same turn? How about if I move it between the same two Pokemon several times in a row?
You have to advance the game state with your actions. If your Psychic Transfers are mindless, then you are not advancing the game state and it could result in a penalty.
Source:
Ultra Prism FAQ (2018-01-19), TPCi Rules Team (2018-02-01)