QIf I select an evolved enemy Galmieux, Omen of Disdain with 3 or less defense when playing this spell with Quick during my opponent's turn, does Galmieux's "Whenever this follower takes ability damage" ability trigger twice?

AYes. This spell first deals 3 damage to Galmieux, bringing her to 0 or less defense. However, she isn't destroyed until the next Confirmation Timing, which occurs after this spell is resolved. This spell then deals 2 more damage to Galmieux, even though her defense is already 0 or less. Therefore, Galmieux takes ability damage twice, and her ability is triggered twice. Note that the same would apply to Servant of Disdain.

QIf my opponent's deck is empty, and I make them put the top card of their deck into their cemetery, do I win the game?

ANo. If you draw a card when your deck is empty, you lose the game. If you put the top card of your deck into your cemetery when your deck is empty, nothing happens.