1. how did the boundaries of the roman empire change?
2. why did the roman empire split into eastern and western parts?
3. how did the boundaries of the byzantine empire change?
3. how did the control of the eastern mediterranean change over time?

The boundaries of the Roman Empire change mostly in terms of expansion into the East and into the West, but only up to a certain point. After this point was passed, the Roman Empire started to crumble and lose territory. 

The Roman Empire split into the Eastern and Western parts because it was easier to manage that way.

The boundaries of the Byzantine Empire changed with the Ottoman threat and the Crusades; it was very varied and is hard to describe.

The control of the eastern Mediterranean was also heavily influenced first by the Crusades and later by the Ottoman empire which had an important fleet.