I received a direct deposit on my bank account (in the US): is it possible to reject it?
Once the payment is in your account, you'll have to contact the person that made it and ask them what to do. I've had a client pay me twice for the same invoice, and they simply said to keep it and apply the overpay as a credit to my next invoice. But the bank typically won't reverse the transaction (nor would the sender be able to have the bank reverse it either). Work it out with the person that deposited the money.
Yes, you may dispute the transaction as you would any other. Contact your bank for their specific procedures.