posprzątać or sprzatac? What's the difference?
"sprzątać" is imperfective, "posprzątać" (or "sprzątnąć") is perfective. That means that "sprzątać" focuses on the process and is more of a general thing, while the other two focus on 'cleaning succesfully' in a specific situation.
When would you use sprzątnąc?
It looks synonymous to "posprzątać" in my opinion. Unless you want to use "sprzątnąć" as an euphemism for assassinating someone ;)
In a previous example, it was "posprzątać w moim/swoim pokoju", so why isn't this one "posprzątać w biurze"? As in, when do you have to use "w"?
Whenever you clean any kind of room, both versions make perfect sense: you either 'clean the room' or 'clean in the room'. Well, in Polish, at least.
The worker has to clean the desk.
Desk would be biurko.