Ok, Pual has a lot of abilities where it allows your opponent to discard a card, destroy a foundation, or commit foundations to negate/cancel the ability.

So for instance if I play an ability and my opponent commits foundations to negate/cancel the ability, can they respond with torn hero, perfect sense of balance or any cards that react to it?

You're not committing your opponents staging area and they have the option to do it or not so does it still work? This also goes for cards being discard and destroyed.

Torn Hero ect won't trigger off of those cards.

It's considered paying a cost, so cards that trigger "when you <do something> as a result of your opponent's card effect..." will not trigger.