Keldeo-GX

Say I have Keldeo GX already in play, and my opponent uses Latios GX's "Clear Vision GX" attack with Power Plant in play. If I play a different Stadium to get rid of Power Plant, can I use Keldeo-GX's "Resolute Blade GX" attack now?

Yes, you can. When Power Plant is removed Keldeo GX's Pure Heart Ability turns back on, and Keldeo GX is no longer hit by the global effect of Clear Vision GX. If an attack does not place an effect on Keldeo GX directly, like an attack that puts an effect that isn't removed when returning to the Bench, it can be removed by reactivating Pure Heart.

Say my opponent uses Trevenant & Dusknoir GX's "Pale Moon GX" attack on my Keldeo GX with "Pure Heart" while Power Plant stadium is in play. If I replace the Power Plant with another stadium during my next turn, does Keldeo GX get knocked out at the end of the turn or not?

If Keldeo GX remains the Active Pokemon it will be Knocked Out. Keldeo GX's Pure Heart Ability *prevents* effects, but it does not *remove* existing effects. If an attack like Pale Moon GX places an effect directly on Keldeo GX, that effect cannot be removed by reactivating Pure Heart; in other words, effects that are removed when returning to the Bench can't be removed by Pure Heart.

What happens if I put a Keldeo GX with "Pure Heart" Ability into play after my opponent has used Latios GX's "Clear Vision GX" attack? Would my Keldeo GX be able to use its "Resolute Blade GX" attack or not?

As long as the Pure Heart ability is not blocked or turned off when Keldeo GX comes into play, it would be unaffected by Clear Vision GX.

If my opponent has used Latios GX's "Clear Vision GX" attack, would my Keldeo GX be able to use its "Resolute Blade GX" attack?

Yes. The effect of Clear Vision GX is placed on each of the opponent's Pokemon, and since Keldeo GX's Pure Heart Ability prevents all effects of attacks done to it by your opponent's Pokemon GX, it is unaffected by Clear Vision GX.