If I play Blaine's Quiz Show and put down "Celebi and Venusaur GX", do I win if the opponent says "Venusaur and Celebi GX" instead?
As long as they get both Pokemon of the Tag Team correct and they include the "GX" part, you shouldn't get that nit-picky about which Pokemon is billed first.
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.
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)
If I use Froslass' "Spiteful Sigh" attack to put enough damage counters on Froslass to leave less than 40 HP on it, will its attack be prevented if Blizzard Town is in play?
No, its remaining HP is checked for Blizzard Town before you place the damage counters onto Froslass.
Source:
Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)