Hm, do the factions have to rent out the embassies, along with the docking bays and security fees?
All territories within Daedalus are leased out to parties, so yes they do. Docking bays, repulsor trams, or other methods of travel are provided with the embassy. Security forces are only hired by ambassadors in the event they do not have their own or prefer hiring security forces of Daedalus over their own. More often than not, that doesn't happen though. Alliance and Imperial embassies are guarded by Alliance and Imperial troopers, for example.