Lampent

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".

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.

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.

If I draw a Pokemon with the "Top Entry" Ability during my first turn of the game, can I put it onto my bench right away?

Sure, but remember you must do this BEFORE it gets into your hand.

If I have a Pokemon with the "Top Entry" Ability in my starting hand at the beginning of the game, can I put it onto my Bench?

No, you may not. In order to use Top Entry it has to be drawn from your deck at the beginning of your turn, but your turn has not started while you're setting up at the beginning of the game.