I assume the Bishops oversee the Priests. If a man becomes a Priest he knows before hand if he gets married he can not advance in the church, is this correct?
Does the head of the EO church come from the monastic ranks exclusively?
Yes, a priest knows that by being married he will not be able to advance to a bishop. But a priest who is not married is very unlikely to become a bishop if he is outside the manastic ranks. It happens, but very, very rarely.
Divorce is not an option for a priest, especially if it was used to advance his "career!" The only way a priest can become single again is if he is widowed.
The "head" of the Orthodox Church is more than likely someone who came from monastic ranks. We don't have a "head" in a Catholic (Latin) sense. The "head" of an Orthodox Church is a bishop who, among the other bishops (a Synod) is the presiding in honor. He holds no special power other than to convene a Synod and to preside over it, but niether he can do anything outrside of the Synod nor can the Synod decide anything by bypassing him. The important distinction here is that it is an honorary title and not one or jurisdictional authority.
That being said, the Church was organized along those lines for the first one thusand years in the East as well as in the West. The concept of "imperial papacy" (or at least the tendencies towards one) were one of the reasons the East stopped communing with the bishop of Rome. We, of course, recognize the Bishop of Rome as the first in honor, but not in jurisdiction. However, communion is impossible because of some theological differences that need clarification.