If I put a Charizard GX in play using Ho Oh GX's "Eternal Flame GX" attack, and my opponent evolves into Porygon-Z and uses its "Initialize" Ability, does Charizard GX go back into my hand?
No. Charizard GX is in play as an "unevolved Pokemon" and so is not affected by the Ability.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)
If I use Ho-Oh GX's "Eternal Flame GX" attack, can I place a Stage 2 Pokemon like Charizard GX from my discard pile directly onto my Bench?
Yes. The attack does not specify that the selected Pokemon have to be Basic Pokemon.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)