QIf I have two copies of this follower on my field, will their abilities negate damage dealt to each other?

AYes, they will.

QIf I play a card that deals damage to my leader on my turn while this follower is on the field, will Sanguine become active for me even though the damage is negated by this follower?

ANo, it won't. Sanguine only becomes active for you if your leader loses defense.

QWill reduction to leader defense caused by sources such as Demonium, Punk Devil be negated by this follower's ability?

ANo, it won't. Reduction to defense is not considered damage.

QWill reduction to follower defense caused by sources such as Agnes Tachyon be negated by this follower's ability?

ANo, it won't. Reduction to defense is not considered damage.

QWhat is ability damage?

AAbility damage is damage from non-combat sources, including damage from spells and follower abilities. Damage from Strike abilities, although triggered by combat, is considered ability damage.