QIf I choose options 1 and 2, can I resolve option 2 first, then select an enemy follower for option 1 after looking at the card I drew?

ANo. When required to select targets for any part of a card or ability, all targets must be selected first. In this case, you must select an enemy follower after deciding which options to choose. Then, the ability is resolved in the order as written.

QIf I select an engaged enemy follower with option 1 of this follower's Fanfare ability, will it refresh at the start of its controller's next turn?

ANo. Although the Fanfare ability's "engage it" effect will not apply to a follower that is already engaged, the "it doesn't refresh during its controller's next start phase" effect will still apply.

QWhen choosing multiple options, can I choose the same option more than once?

ANo, you can't.