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)
Let's say I have two copies of Garchomp & Giratina GX in play, and one of them has a Double Dragon Energy and a basic Psychic Energy card attached to it. If I play Tag Switch, am I able to select only one of the Energy being provided by Double Dragon Energy, so that I may also move the Psychic Energy too? Or if I had two Double Dragon Energy cards attached, could I pick one Energy from each Double Dragon Energy for Tag Switch and move both cards?
Yes, you can either select 1 Energy from each Double Dragon Energy to move both cards, or you could select 2 Energy from one Double Dragon Energy to move just one card.
Does "Recycle Energy" go back into your hand if you discard it as part of a retreat cost? Does it go back into your hand if it's attached to a Pokemon that gets knocked out?
Yes in both cases. But don't be discarding it from your hand as part of an effect or Trainer cost and expect to get it back though. Also, if something sends Recycle Energy to the Lost Zone, you won't get it back from there.
Source:
Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)
Is the old print of Recycle Energy from Neo:Genesis legal for tournament play since it has slightly different wording that the latest version from SM:Unified Minds?
No, the wording is different in that the old version works after Recycle Energy has reached the discard pile, but the new version works even before Recycle Energy reaches the discard pile. You must use the newer version of the card in tournament play.
If I have a Memory Energy attached to an Incineroar that evolved from a Litten with the "Caturday" attack, with Persian's "Gathering of Cats" Ability are all my Incineroar's attacks now free?
No, it doesn't work like that. Memory Energy lets you USE attacks from its previous Evolutions, but it doesn't GIVE it those attacks. Therefore, Gathering of Cats would have no effect on the Incineroar.
If an Evolution Pokemon has been put directly into play by using Greninja & Zoroark GX's "Dark Union GX" attack can I attach Triple Acceleration Energy to it?
Yes, as long as the Evolution Pokemon says "Evolves from..." on it.
Source:
Unbroken Bonds FAQ (2019-04-19), TPCi Rules Team (2019-05-02)