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 at the beginning of your buy phase, after which point you cannot play more cards. If you have played any copper, you cannot buy Grand Market, and if you have already bought Grand Market you are into your buy phase already and cannot play any coppers.
There are a few exceptions:
Cards that give you an extra Buy phase, (e.g., Black Market, Villa). You can play all the Coppers you want in one Buy phase and buy Grand Market in another.
Cards that remove treasure cards in play during your Buy phase (e.g., Mint, Bonfire, Counterfeit, Mandarin). If you are able to remove Coppers after playing them (trashing them, or something else like Mandarin), they are no longer in play and you can buy a Grand Market.
Of course, additional exceptions may be created...