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.
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.
If I have a Klawf ex with "Counterattacking Pincer" Ability and Rugged Helmet attached to it, what happens if it gets damaged by an opponent's attack from a Fusion Strike Pokemon that has a Fusion Strike Energy and a Double Turbo Energy attached to it?
The Counterattacking Pincer ability and Rugged Helmet are triggered simultaneously, so you may choose the order in which they are applied. If you choose the Counterattacking Pincer ability first it will fizzle due to Fusion Strike Energy. However, if you choose to use Rugged Helmet first you can put the Fusion Strike Energy into the opponent's hand and then you can use Counterattacking Pincer to discard the Double Turbo Energy.