When a customer pays me and I deposit that money, I Receive Payment" in the invoice, and allocate that same payment when I add the deposit. Am I doubling the payment?
No, you are not doubling up. When you receive the payment it is posted to Undeposited Funds. Then you record what you did with that payment, which is the deposit. This gives you the chance to group several payments into a single trip to the bank, or to deposit multiple payments among multiple bank accounts