QIf I evolve this follower with its Fanfare ability, can I evolve another follower using its evolve ability in the same turn?

AYes. Although you can only activate one evolve ability per turn, other abilities that evolve followers do not count towards this limit.

QIf I can't select an amulet on my field with this follower's Fanfare, can I still draw a card and evolve this follower?

ANo, you can't.

QIf my main deck, evolve deck, and glory card are based on the same universe and my leader card is Mejiro Palmer [Go Ahead and Laugh], does it fulfill the condition for this follower's Fanfare?

ANo. If your leader has both a class and a universe, you must declare which your deck is based on before the start of the game. In this case, you would have chosen universe for Mejiro Palmer [Go Ahead and Laugh], meaning it does not count as a Havencraft leader.