The math does not include atmosphere friction and mechanical frictions within the station. ISS has to compensate for them artificially and so has the Citadel.
Drag, sure. Not sure what you mean by "mechanical frictions within the station." Anyway, what does that have to do with the mass of the Citadel?
Reducing the station's mass with a mass effect field would make the drag problem worse, not better. Actually, it might be a wash since when the air molecules enter the field they'd lose mass too, but mass effect physics are so wacky it's hard to say.
We don't know where the beam is in London. There are no landmarks I recognize around where it is (not a London resident so can be mistaken). I'd say it's quite possible for the Citadel to be directly above London and maintain position artificially until Crucible fires. After that the station is switched to an emergency mode and only uses power to keep itself on orbit.
Keeping itself in orbit isn't the issue. If it's stationary over London at that altitude it doesn't have anything like orbital velocity. Emergency mode would have to establish the orbit first.