Paris hosted the Federation President.
San Francisco hosted Starfleet HQ.
Lisbon hosted the Division of Planetary Operations (global power grid).
Berlin and Canberra hosted Vulcan compounds.
But that bit doesn't mean much -- foreign states establish diplomatic missions called
consulates in large cities throughout a host state, and such consulates are subordinate to the embassy in the host state's capital. So the fact that Vulcan has consulates in Berlin, Canberra, and San Francisco just tells us that those cities are apparently not United Earth's capital.
And how many other times was the president's office shown to be in Paris? And is that the President's only office or does he have other offices on Earth and maybe other planets?
Nobody has mentioned this, but it is worth noting that a presidential administration may be spread out across multiple buildings -- even just the direct presidential office. The U.S. President famously works in the West Wing of the White House -- but a large percent of staff members who work for the
Executive Office of the President (i.e., they work directly for the President rather than for one of the United States departments) actually work out of the
Eisenhower Executive Office Building next door.
So it is possible that the Federation's equivalent to the Executive Office of the President (i.e., the administrative division of government employees who work directly for the President rather than for a specialized department or agency) may indeed span multiple buildings -- perhaps across Paris, or even perhaps across Earth. There's nothing in the canon to contradict this, though of course no such thing is established.
For the record, the novels have mostly established the Palais de la Concorde as the Federation's capitol building, housing both the offices of Members of the Federation Council, the offices of Federation Council committees, and the offices of the President and their direct staff. Personally, I think the number of people involved in that kind of setup would be too large to fit into one building, but I guess the Palais is supposed to be
big. Though even though novels have not
precluded the possibility of there being other such governmental buildings. (I like to imagine that there are Federation Councillors whose offices are in the Sarek Council Office Building or some such, but that's just me.

)
It seems very unlikely that the seat of the Federation's political power is something that would have been trivial to the writers.
It is
incredibly trivial.
Star Trek is about starships in outer space; it is not
The West Wing With Artificial Gravity. How important was the fact that the capital of the Galactic Empire was on Coruscant to the original
Star Wars trilogy? Not important at all -- because the
Star Wars OT was about the battlefields, not the halls of power.
It is a minor detail to
Star Trek VI: The Undiscovered Country, to "Homefront," and to "Paradise Lost," whether the President is in Paris or some other city. It has exactly zero impact on the plot or characters; there no meditations on Parisian history and how that impacts the plot happening right then. Nobody expresses attachment to Paris as a location. President Jaresh-Inyo doesn't declare, "By Jove, I can't sign this Declaration of a State of Emergency! I love the freedom Paris represents too much to do that!"
Really, the Federation President's office could have been in
McMullen, Alabama for all the impact its location had on the stories that featured it.
Its possible an organization like the Federation could have rotating capitals as well. Back and forth between at least the three founding worlds.
Personally, if I were re-designing
Star Trek from the ground up, I would have the Federation capital be on a previously uninhabited planet settled by all of the founding members of the UFP. That world would gradually develop its own unique identity and status as a Federation Member in its own right, but that way no one of the founding Federation Member would ever dominate the UFP the way, say, England today dominates the United Kingdom. I liked it when David Mack posited Deneva as the capital planet of the
Galactic Commonwealth, but that's just me.
That worked out so well the last time the USA had an isolationist trend. <sarcasm>
In fairness, given who we've allowed to take over the Oval Office, it just may be that it's the
rest of the world that has to intervene to prevent the aggression of
American fascism soon.
1) No. As others have outlined, the United States Congress does not answer to or work for in any way the President of the United States.
2) The United States Constitution came into effect on
4 March 1789, not "always."
But we know very little about how politics work in the UFP except it appears to be unicameral in nature. The DSN two-parter "Homefront" and "Paradise Lost" doesn't seem to give any clear indication on whether the President is elected by the Council members from their members or by General election.
For whatever it's worth, I am aware of only one sovereign state in real life for whom a non-ceremonial President is elected by the legislature: the Republic of South Africa, whose National Assembly elects the President of the Republic of South Africa from amongst its members. This is because the office of South African President evolved out of the office of Prime Minister during the apartheid era. In almost every other state whose legislature elects its President, the President in question is a ceremonial figurehead like the Federal President of Germany.
The pocket veto is only possible when it cannot be overridden. Therefore, it is absolute in its effect.
But it can only happen if Congress choses to adjourn. If Congress choses to convene, it cannot occur. It can also be overridden in practical effect if not in legal technicalities if Congress chooses to convene, pass an identical Act under a new bill number, and then override the subsequent veto or to refrain from adjourning so as to prevent the use of a second pocket veto.
The point of mentioning all this is not to say that there are not ways for a President to exercise power against the will of Congress or to prevent bills from becoming law that a majority of Congress supports; there are. The point of mentioning all this is to re-affirm that the President and Congress are co-equal branches of government under our constitutional system.
Or at least, they
would be if certain Members of Congress in the majority party weren't so terrified of the current White House occupant's political influence with their constituents (or so enthralled with his willingness to embrace graft and corruption for themselves and their capitalist friends) as to be unwilling to actually
exercise the constitutional checks and balances against the presidency granted to them by the Constitution.
Another peculiar thing about Benjamin Lafayette Sisko is his middle name Lafayette: it is French and it is of major significance to the United States. There is Lafayette Square, named after the Marquis de Lafayette, the French General and military leader; it contains a statue in his name. The square is only 3.47 km or 2.16 mi away from The Pentagon.
Dude, we get it -- you like France.
