My opponent has Galarian Weezing with "Neutralizing Gas" Ability in play. Is the "Top Entry" Ability still allowed as a method of benching a Pokemon, or can it not be benched?
You can still bench it. The Top Entry Ability is used before the Pokemon with that Ability is "in play".
Source: TPCi Rules Team (2021-01-21)
Is a Pokemon put into play via the "Top Entry" Ability deemed Stage 1 regardless, and not a "Basic" Pokemon as they're technically a Stage 1 Evolution?
It retains its Stage, but it is not an evolved Pokemon ("a Pokemon in play that has another Pokemon under it") even though it remains an "Evolution Pokemon" ("a Pokemon card that evolves from a lower stage Pokemon"). Note this difference in terms because it is important in some interactions.
Source: TPCi Rules Team (2021-01-21)
If I play a Pokemon with the "Top Entry" Ability and it goes to the bench as a Stage 1, what happens if I then use Devolution Spray Z?
You can't use Devolution Spray Z on it since although it is an "Evolution Pokemon", it is not Evolved because there is no Basic underneath it. Either you can't play the card, or if it has already been played (it's no longer in the hand) another target will have to be chosen. If there are no other legal targets, then the play has to be reversed.
Source: TPCi Rules Team (2021-01-21)
If I play Lysandre {*} when my opponent has Shiftry's "Shifty Substitution" Ability in effect, does Lysandre {*} go to the Lost Zone or not after it has been played?
Shifty Substitution does not affect the Prism Star rule, so Lysandre {*} would go to the Lost Zone.
Source: TPCi Rules Team (2020-12-10)
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)