Hi HimSelf,
I don't think we you can process another person payments (eBay, the creator of Paypal) don't do that, instead I think you can ask your users for a payment (payment request), when you send the user a bill with an amount, and they click yes or not to pay it.
Having transactions on the site means a lot of work on that plugin, you need to double check everything and trust on your users. If you're an eBay user, you probably has faced some problems already (I did), and knew how easy is to bogus the system.
Examples:
As seller you could mark an item as "send" but never sent it.
As buyer, you could claim the packet you received was empty.
As buyer you could buy something and never pay for it and even mark it as paid.
eBay can control paypal, which controls your money for a few time. They're also big and can assume losses, they make enough money to have some bad-users which game the system. This could be a very big problem for small/medium websites, usually the community auto-moderate itself, but you should have to put a hell of terms&conditions and tell you're only the man in the middle and you are not responsible for anything. Should a lawyer check it. When money is included everything gets dirty...
We want to develop the tools, and make it easy for everyone, we should study this topic deeper