If I have 2 {P} Energy and an Aurora Energy or a Rainbow Energy attached to a Galarian Articuno and I use its "Psylaser" attack, do I have to discard the Aurora or Rainbow Energy since I'm not using them as {P} Energy?
Yes. Aurora and Rainbow Energy provide all types of Energy all the time when they are attached to a Pokemon, even if you don't want them to.
Source: TPCi Rules Team (2022-10-13)
If I use Dusknoir's "Special Transfer" Ability to move an Aurora Energy to another Pokemon, do I have to discard a card from my hand per Aurora Energy's text?
Special Transfer is "moving" the Special Energy to another Pokemon, not "attaching" it like you would from your hand. So since the Aurora Energy is already in play you do not have to discard a card from your hand in this situation.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)
When my opponent has Goodra with the "Slimy Room" Ability in the Active Spot, if I try to attach an Aurora Energy to one of my Pokemon and I flip tails, do I have to discard a card for the cost of Aurora Energy too?
No, since the flip happens before it is attached, if Aurora Energy is discarded you do not have to discard another card along with it.
Source: Fusion Strike FAQ; TPCi Rules Team (2021-11-11)
Can you use Frosmoth's "Ice Dance" Ability to attach Aurora Energy?
No. Because Aurora Energy does not count as any type while it is in your hand.
Source: Sword & Shield FAQ (2020-01-24), TPCi Rules Team (2020-02-06)
The discard cost on Aurora Energy only applies when attaching the card from your hand. If you attach it from somewhere else, you don't have to discard a card from your hand.
Source: Sword & Shield FAQ (2020-01-24), TPCi Rules Team (2020-02-06)