QIf this follower's defense is reduced to 0 by ability damage during my turn, will its "Once on each of your turns, when this takes ability damage" ability trigger?

AYes. The ability will trigger before the card is destroyed.

QWhat is ability damage?

AAbility damage is all damage except for damage dealt by two followers in combat or by a follower attacking a leader. Damage from Strike abilities, although triggered by an attack, is considered ability damage.