Go to Admiral Quinns office on ESD and talk to the Fed Ambassador there (I forget his name). He is with the rom ambassador and someone else. He gives you the store option where you select the BOFF for level IV diplomacy.
They asked about "The Dominion Faction". As there is no such faction now or forthcoming, It would be logical to think they were referring to the Jem'Hadaar Faction. For the incoming faction, They should not be a part of it. I would be amenable to doffs and boffs though.
Those 4 doors don't open. You just look throught he cameras. There is a left turn after the 4th door and at the end of that left turn is another door you go through.
Visit the romulan ambassadoe by Admiral Quinn, By the Security Officer in First City, or on DS9 by the shipyard. They will give you a mission to go to New Romulas.