how is the remainder of the Lamb divided up and distributed?
It's divided into four portions (the fraction). One of them is placed in the chalice as it is (the commingling), and two of them are divided by the priest into small particles.
What happens to the other portions (the piece for the Theotokos, the 9 ranks of the angels, and the pieces used to commemorate the living and departed)?
They are not consecrated, but are still ordinary bread, and are added to the chalice after the communion of the people has taken place.
As far as the wine is concerned, is it considered sanctified once the Body of Christ is placed in it (I would assume so), or would the priest consecrated the wine in one chalice, and then add a bit of it to the other chalices?
The wine is consecrated in one chalice, and then added to the others at the fraction.
According to the Russian tradition, wine is not consecrated merely by having the Body placed in it; hence, at the Liturgy of the Presanctified, the wine in the chalice is ordinary wine and not Blood.