I'd rather keep my answers simple just in case.
First - if its a theology of the Greek Church, it will also be of the Russian, Serbian, Antiochian, etc - all of the EO Churches. Almost all of our theology is likewise shared with OO. You will find variations is musical style, pious customs, and emphasis on favorite Saints to sometimes differ, but theology must always be the same for all EO Churches.
We do sometimes use the term "transubstantiation". The bishop explained to me that we must not invest the term with some of the philosophy and teachings of Catholicism. Basically - we believe that the bread and wine are transformed by the power of the Holy Spirit to be the actual Body and Blood of Christ - and that this is a mystery. Any attempts to say almost anything more about the change or explain more fully just what that means are usually something we reject. So we don't get into scientific analysis or physical vs spiritual and all the explanations of how the spiritual works that many (including Protestants) explain. It. Just. Is. Because Jesus said so.
We offer the bread and the wine - the fruits of the earth (which God gives) and through our labor we harvest and prepare it and offer it to God.
And yes, we are mystically joined to the offering Christ made "once for all" on our behalf. Just as every year at Pascha we are joined to the mystery of the Resurrection, every Sunday (when we normally celebrate the Divine Liturgy) is a "Little Pascha" in that way. We are always being re-connected.
I can't confirm the other details.
That does put me in mind of one possible difference. Doesn't Catholicism focus on the crucified Christ? We are mystically united to the RISEN Christ in the Eucharist. So that might affect the answer to some of your questions?
Thank you this is awesome! I appreciate this. I think we basically beleive the same thing here. The Catholic Mass both the death and resurrection is empathized. We proclaim the death and resurrection through the mass until christ comes in the end. The elements of bread and wine are separated signifying Christ death and separation of his body from the blood on the cross but we receive the Resurrected Jesus and proclaim that resurrection in the Eucharist also in the prayers. Does that make any sense?
This is from eucharist prayer 1 in the Roman Canon of the Ordinary form:
"We proclaim your Death, O Lord,
and profess your Resurrection
until you come again."
Or another Optionis
"Save us, Savior of the world,
for by your Cross and Resurrection
you have set us free."
"Therefore, O Lord,
as we celebrate the memorial of the blessed Passion,
the Resurrection from the dead,
and the glorious Ascension into heaven
of Christ, your Son, our Lord,
we, your servants and your holy people,
offer to your glorious majesty
from the gifts that you have given us,
this pure victim,
this holy victim,
this spotless victim,
the holy Bread of eternal life
and the Chalice of everlasting salvation.
Be pleased to look upon these offerings
with a serene and kindly countenance,
and to accept them,
as once you were pleased to accept
the gifts of your servant Abel the just,
the sacrifice of Abraham, our father in faith,
and the offering of your high priest Melchizedek,
a holy sacrifice, a spotless victim.
n humble prayer we ask you, almighty God:
command that these gifts be borne
by the hands of your holy Angel
to your altar on high
in the sight of your divine majesty,
so that all of us, who through this participation at the altar
receive the most holy Body and Blood of your Son,