To answer your first question, there isn't any established system of peerage in the Empire, or even political rankings. There is the Elder Council who seem roughly equivalent to the Roman Senate in the late Empire (a piece in http://www.imperial-library.info/content/brief-history-empire uses the bit of real-world history of a change in the law who gets to be in the Council meaning it was suddenly just made up of those who could afford it).Your best bet is to look to real world Empires and just invent wherever you please.
In regards to your second question, there are few examples of pure "politician"s. There would be bureaucrats who work in the Imperial household, the powerful, rich and wise in the Elder Council, and then representatives from outside the city, such as Cyrodiil's counts, or the many Kings and Queens of the provinces. Anyone can get involved in politics, but as there is no system of election, "politician" is not a job.
Thirdly, the Imperial College probably does exist outside the Arcane University. Their education is probably only "scholarly", as you say, or as Arcane Matters belong in the Arcane University.
Finally, Entrance into the Elder council is no doubt won through already exerting some strong political influence, be it financial or ancestral. Your best bet would be to read the Brief History, and the two Pocket Guides on this matter.