QMy leader's defense is 11 and I have no followers on my field, while my opponent only has a Rabbit Necromancer. I play this follower during my turn and use its Fanfare to destroy Rabbit Necromancer, triggering Rabbit Necromancer's Last Words and bringing my leader's defense to 9. Does this follower's other Fanfare then take effect and give my leader +5 defense?

ANo, it doesn't. When this follower's Fanfare destroys Rabbit Necromancer, Rabbit Necromancer's Last Words will trigger and becoming pending. When both players control pending abilities, the active player resolves theirs first. In this case, you are the active player, so you would resolve this follower's other Fanfare. At this point, since Rabbit Necromancer's Last Words have yet to take effect, your leader's defense is still 11, so it does not gain +5 defense.

However, if you were to somehow summon this follower during your opponent's turn in this same scenario, Rabbit Necromancer's Last Words would resolve first as your opponent is the active player, so your leader could gain +5 defense from this follower's Fanfare, provided you chose to resolve the select and destroy Fanfare first.

QCan I only play this follower's activated ability when it's in my cemetery?

AYes, that's correct.

QCan I choose the order in which I resolve this follower's two Fanfare abilities?

AYes, you can.

QIf I can't select an enemy follower on the field for this follower's first Fanfare, can I still draw a card?

ANo, you can't.