On the buy page, what is the purpose of the "stage" and "payment" columns?

Hello,

Those columns are for tracking and managing your auctions.
This way you know what auctions were paid of and which auctions were not received yet, and so on.

For example, if you paid for some auction but did not receive it yet, then you might want to ask a seller about its status or maybe submit a fraud report with PayPal or whatever payment method you used.

OK, so I can use the fields to manually track the status of any auctions that have closed. I just wanted to make sure myibay wasn't going to try to automatically pay for my auctions, if I used those fields. Thanks.

Correct, it will not automatically pay. It does not even know your PayPal account or anything like that.
No worries about it.