If i add a new address to my paypal account and make it the primary address will a payment still go in from the other address on my account?
You mean email address ? if yes, if you add new email id to your paypal, you can receive payments using both emails. The notification emails from Paypal will go to your default email address (which you can set in your profile)
Yes, your payment will go to that address. I'm uncertain whether it will show up in the buyer's admin panel as the address they sent their payment to though. It might say your "main" paypal email. But then again I'm not 100% sure.
Just to add, even if it is mailing/physical address change, it would be accepted as long as it is within the same country. You may have to provide documentary evidence of the address change but that should not be a big issue.
Payment can be sent to either of the addresses. Login could be done only using the primary address and all payment notifications would be sent to the primary address. In short, primary address is your main mail address for all paypal purposes.