QIf I look at the top card of my deck and it's an Omen card, can I choose not to add it to my hand?

AYes. In that case, you would not reveal it and simply return it to the top of your deck.

QIf this follower takes ability damage during my turn that brings its defense to 0, does its "whenever this takes ability damage" ability still trigger?

AYes, it does. You would resolve the automatic ability after this follower 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.