If I'm using Scizor's "Punishing Scissors" attack and one of my opponent's V Pokemon has Forest Seal Stone attached, does my attack do an extra 50 damage for it?
No, the V Pokemon does not *have* the Star Alchemy Ability, it only can use it.
Say my opponent has 3 Genesect V on the bench and Path to the Peak is in play. If I attack with Scizor's "Punishing Scissors" attack, do I do 10 damage or 160 damage?
When Path to the Peak is in play Genesect V has no Abilities, so Punishing Scissors would only do 10 damage in this situation.
Do I have to meet the energy requirements for the attack I choose with Mew ex's "Genome Hacking" attack?
No, you do not have to meet the energy requirements for the attack. However, if the attack says you must do something or the attack does nothing, that part still has to be done.
After time is called at the end of a match, what happens if I use Medicham V's "Yoga Loop" attack during the "plus three turns" part?
If you use Yoga Loop when time is called during your turn, you would then get "Turn 1" instead of your opponent. Likewise, if you use it during Turn 1 you would also get Turn 2 and your opponent would get Turn 3, and so on... However, if you use it on the final turn of the match you do not get an extra turn.
If my opponent flipped heads for Nymble's "Slight Splash" attack on their previous turn, what happens if I use Quaquaval ex's "Exciting Dance" attack? Does Nymble get switched out to the bench or not?
The effect of Exciting Dance is done to the protected Nymble, so Exciting Dance would not move it to the bench.
If I have 5 Pokemon on my Bench and Lunatone with "New Moon" Ability and Solrock are in play, what happens if my opponent plays Collapsed Stadium? Would I have to discard any Benched Pokemon or does "New Moon" prevent that?
The effect of Collapsed Stadium is being done to the player's bench size, not to the Pokemon on the bench; so New Moon would not protect them and you would have to discard Benched Pokemon.
Would a Solrock coming into play on the bench receive damage counters from Gapejaw Bog if a Lunatone with "New Moon" Ability is in play but the Ability is not active yet (it requires Solrock to also be in play)? Or what if you put that Lunatone onto the bench while Solrock is already in play?
New Moon activates immediately when it's condition is met, so in either case the 2 damage counters from Gapejaw Bog would be prevented.