Arno died. I think the Head Priest killed him because Arno's action on the day of the ambush is endangering Head Priest's interest. Him not telling Fran that Head Priest is present, just in his hidden room, instead telling that he is absent made confusion and almost get Myne abducted by Bindelwald. All of his action is not intended to damage the Head Priest, just for Fran, but because of his action that day, and then after telling Head Priest about Fran's dark past, I think Head Priest judged that he have grudge to Fran and it will obstruct his future relation with Myne.
Climbing the Towering Stairway = Death. If you read arc 3 v1, you would understand what that means when the phrase appeared again for Rozemary.