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.
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.
Can you use more than one Orbeetle VMAX’s “Eerie Beam” Ability per turn?
If a different Orbeetle VMAX becomes active you can use its Eerie Beam Ability, but each Orbeetle VMAX can only use its Eerie Beam Ability once per turn.
Source:
Vivid Voltage FAQ (2020-10-31), TPCi Rules Team (2020-11-12)