If it is reasonable for the characters to do so, can a character make an unfavourable trade in the marketplace with another player/character? Or, if not, then can said character request a service instead of rupees, or the full rupee amount?
The short answer is yes. Characters can exchange between themselves any items, rupees, or services that are tradeable. So long as both parties agree on the exchange, and all items can be traded (ie., you can't trade the ability to use Spin Attack), it's fine.