“What is the Eastern view of the relationship between the priesthood and the episcopacy?”
The priest is the “celebrant” at the Liturgy and is the bishop’s representative in the parish. The authority to have the Divine Liturgy conducted in a parish is represented by the antemision. The bishop has total authority over the priest.
“But I have a dim memory from childhoold of hearing that the Eastern Church (some of it?) typically gives Baptism, the Eucharist and Confirmation to infants at the same time. Does the bishop do all this (assuming what I heard was correct)?”
If a bishop baptizes a person, the bishop will likely also chrismate that person and give him or her first communion. Ordinarily, all three sacraments are administered at the same time and by a parish priest and in the usual case this is done in infancy.
Sounds to me the same as the Western Church, but I don't see that it answers my original question in regard to your "the Latin notion that the priest (as opposed to a bishop) is Alter Christus." 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)?