How does making a payment to myself work? I see how to do it, but what is the conversion based off? Who is setting that rate and who am I actually buying XRP from if I do it that way? From Opencoin?
It works the same as any payment. The pathfinding engine looks at what assets you have and what assets the recipient will accept and then it looks at all the liquidity available in the ledger (ripple paths and order books) and finds the cheapest path(s) to make the payment. The payment can even pull from multiple paths and multiple order books.
Also, what is the difference between making an XRP payment to myself but paying with USD and making a USD payment to myself, which does not seem to be possible (I get a message "No Path Found")?
The payment interface requires you to select the recipient account (and destination tag if appropriate), destination currency, and destination amount. You can then pay with any currency you hold, provided you have a sufficient amount and there's sufficient liquidity available in the ledger. (There are a few exceptions. For example, you can't make a payment to yourself with the same source and destination currencies.) This is basically Ripple's primary feature.
Actually, now I just tried to send a payment to myself and got an error: Path could not send full amount.
That's a bug and starting Monday, fixing it will be my top priority. (It seems somehow the pathfinding engine selects on order book and the path selection engine checks a different order book to see how much money the path can deliver. I have good logs and reproducible test cases.)