Greece had an empire phase prior to the Roman Empire, why didn't this create a diaspora of Greek speakers across the Mediterranean? Is it due to the differences in administration of the empire?
Um, it did. Greek dominated the entire eastern half of the Mediterranean all the way through until the loss of those territories under the rise of Islam. Greek was perhaps more successful at displacing other languages and remaining dominant than Latin was, given that Latin never really gained daily usage in the eastern half of the empire, except in government, some legal, and military contexts.
Also, what was the role of the Bible and the schism in it?