Feds get Dofffs at Starfleet Academy. You can find out exactly where from here.
I can't answer your other questions about Rom Doffs, as I've never done any Doffing with my 1 Rom character. I assume there's only 1 Rom Doff vendor.
As far as other Vendors for Doffs, you can buy Doffs from your Fleetbase as well.
STO is about my Liberated Borg Federation Captain with his Breen 1st Officer, Jem'Hadar Tactical Officer, Liberated Borg Engineering Officer, Android Ops Officer, Photonic Science Officer, Gorn Science Officer, and Reman Medical Officer jumping into their Jem'Hadar Carrier and flying off to do missions for the new Romulan Empire. But for some players allowing a T5 Connie to be used breaks the canon in the game.
Only one Romulan doff vendor, Valaar, at New Romulus Command. She offers to you the duty officers that either Lt. Ferra or Lt. St'ass offer at the respective Starfleet/Klingon academies, where they are found. This depends on the faction you have allied with.
There is no Romulan Personnel Officer, however, in the room where Valaar is found there is a console on the near wall that performs the same function and allows recruitment and exchanges.
As discussed for Fleet Credit, you can purchase doffs from the Fleet Starbase, and holdings.
There are many other ways to acquire them, but that's another matter.