If Dusknoir with the "Spectral Breach" Ability gets Knocked Out while Recycle Energy is attached to it, does the Recycle Energy go back to my hand or not?
No, Spectral Breach is still in effect when the cards are going to the discard pile, so the Recycle Energy would be discarded.
Source: TPCi Rules Team (2020-11-12)
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)
Does Recycle Energy go back into your hand if it is discarded by your opponent's Giratina's "Dimension Breach" Ability?
Yes it would.
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.
Source: TPCi Rules Team (2019-08-01)