Hi Donna,
 
The administrative creation of the Eastern Roman Empire was accomplished by Diocletian in 293 A. D. when he instituted what was called the Tetrarchy. The Tetrarchy soon fell apart, but the division of east and west was permanent. Subsequent historians obviously coined the name Byzantium for ease of identification. A good deal of the Eastern Roman Empire was essentially gobbled up by the rise of Islam in the east, but Byzantia, as you know, continued till 1453.
 
Perhaps the seventh kingdom was the Ottoman Turk empire, but since I see no continuity here with the imagery of Daniel 2, I have to discount this idea. There is continuity, however, in the church of Rome, which was made the official religion of the empire by the Christian emperor Theodosius in 391 (the year he banned all pagan worship).
 
I believe all our present questions will be answered fairly soon. Thanks for the discussion, and I know you will be staying tuned.
 
Your brother in Christ,
Matt in Hayward