Yes - there is a small usage difference, but that is a nuance of no real importance until C2 level, imho. ;)

(Poles would generally use "Nie ma mnie w biurze" to indicate they are not in the office(for the day or at least some longer period of time), while "nie jestem w biurze" would be used more like "right now I'm not in the office", for example to inform they can't do something right now over phone - "nie mogę tego sprawdzić, bo nie jestem w biurze"(I can't check it, because I'm not at the office[right now]), but it does carry the point across anyway, so… ;) )

Nope, that won't make any sense.

Unless "Nie mnie w biurze urzędować". But it's another kettle of fish :)