Non sequitur since None of those adjacent States ceded their territory to the central Government for the purpose of the Capitol. Retrocession of everything outside the Mall,White House, Supreme Court, Capitol, Monuments, etc would be the best way to deal with with the proper representation. Definitely preferable to Statehood, which is offensive enough to need a Constitutional Amendment to be legal and patently unfair for other States, especially the larger ones, as well or the very idea that a Capital State should have been formed from the territory of other members. I'd prefer to create a new Capitol in the very center of the nation from ceded territory.
As far as the Federation, definitely seems representative democracy, though the size of the Federation Council has never been established has it? Trek Apocrypha like Spock's World had T'Pau as the head of Surak's House and Spock as it's heir after Sarek. That same novel had several explicit references to representative democracy, though there was also a public referendum. None of it is in any way Trek canon, of course.