What are the chances of a mer, especially an Altmer, in Cyrodilic politics? What would the situation have been like after the Aldmeri Dominion's formation and its separation from 4E 29? And what would the situation have been like after the Great War in 4E 175?

Would it be absurd that an Altmer could be an influential political figure or noble in Cyrodiil? The Count of Cheydinhal was a Dunmer, would his line still hold the title or would he have had it stripped from him and exiled? How far does Imperial mistrust of Altmer, and Mer in general, run? Would any Altmer even be permitted in Cyrodiil?

Chancellor Ocato?

Was assassinated in 4E 10. I want from 4E 29 (when the Summerset Isles broke off from the Empire) and on, and from 4E 175 (after the Great War) and on.

There's an Altmer Legate in the Imperial Legion participating in the Civil War, so I'd say it's pretty apparent that Altmer are not only permitted in Cyrodiil, but can rise quite high through the ranks even after the Great War. Though that may not be what you're looking for considering you're asking about politics and nobility, but to be fair there is quite a bit of politics in choosing military officers.

Also, considering the Thalmor has a nasty habit of.... "rehabilitating" those who they don't agree with in a way that makes most people nervous, I'm pretty sure that Cyrodiil probably has its fair share of Altmer refugees seeking asylum within the Empire.

Even if there aren't any refugees flocking into its borders, the Altmer can definitely come into Cyrodiil. The White-Gold Concordant pretty much allows the Thalmor to goose step wherever they please within the Empire, which is a large part of the Civil War in Skyrim.

As far as political leaders go, I'm sure there are some, but I can't name any. I think the political body of the Empire realize that the Thalmor are a fringe group running the show, and do not accurately represent all individuals of Mer heritage.