e if you have not signed a specific representation agreement I see no problem with either situation you have posed. It would be…. polite for you to at least inform the agent you are working with that you are working with someone else. If they inquire why you can let them know. Any buyers agent can go ahead and reduce the commission they receive and rebate it back to you (yet most of thier brokers will not allow that).
It is all negotiable. I never understand why more buyers do not demand that.