While you wait for more targeted answers, here's some previous threads with general information on the shifting Roman capitals:

• How did Constaninople replace Rome as a capital in the Byzantine Empire? - 22 comments, over 10 months old.
• The commenters in this thread focus on the disadvantages of Rome's position in comparison with capitals nearer to the frontiers.
• What happened to Rome as a city after the Constantine moved the capital to his "New Rome"? - 20 comments, over 1 year old.
• This goes deeper into the experience in the city of Rome as other cities were delegated to various administrative tasks and the Rome became less and less the heart of the empire.
• Besides Rome and Constantinople, what were the capitals of the Roman Empire? - 5 comments, over 7 months old.
• This thread draws attention to other cities and their contributions and value to the empire as the city of Rome became less important.
• Why was Rome not made the capital of the Western Roman Empire when it was created? - 9 comments, less than 1 month old.
• The commenters here go into Roman politics at the time of Constantine and his successors, noting tensions between the Senate (based in Rome) and the emperors which even led to a civil war being fought between the two.