If you buy the Grand Market in your turn, can you then use spare copper to buy something else? Or does doing so forbid you from having bought the Grand Market?
No. Technically, you play all treasure cards you want to use
The pseudo-exception is in the case of Black Market, which adds an extra buy phase. You could buy a Grand Market from a Black Market play, and then play coppers to use in your end-of-turn buy phase.