“For the Eastern Church, is the priest not considered to be alter Christus in the celebration of Divine Worship and in Confession (not sure what the Eastern term would be)?”
Absolutely not. The “Alter Christus” idea is completely foreign to Orthodoxy except in an +Ignatius of Antioch sense and then only with regard to a bishop...and I doubt any Orthodox hierarch would think of himself, much less call himself an “Alter Christus”.
In Confession (you got the right term) the priest is simply a witness for the Church and acts as a spiritual father for the penitent. In no way does he assume any role like Christ. There is no “Absolvo Te”, at least not in the Greek confession rubrics. By the way, any person may hold the offikion of confessor, not just priests. There are many holy monks and nuns who have been authorized by their bishop of hear confessions and act as a spiritual father/mother.
So nuns can administer the Sacrament of Confession in the East?
What is the Greek use? Is there some prayer or formula that's customary?
So the "Office" of confessor resides in the bishop and he may delegate as he sees fit?
I'm assuming the whole derives from "whose sins you shall forgive," -- I'm just trying to be clear on the development and understanding. (I do appreciate your taking the trouble to explain!)