One thing worth noting is that the proof of purchase will not be in the songs you download, but the receipts you get from the online music store. Depending on the music store, they will either e-mail you receipts for your purchases or let you download the receipts from your online account. The same applies for goods bought at a shop. If you walk through the security gate and the sirens go off, the first thing a security officer will ask for is your receipt to show that you bought the goods you are carrying. The shopping bag is not proof of purchase for what's inside. The difference with the online shop is that the receipt will be in your name, like with software licenses.
It's up to you then what you do with the songs, whether you convert them into another format, edit their tags, etc., as long as you don't violate the copyright restrictions (e.g. makes copies for other people, broadcast them in public, etc.) However, just as high street shops will generally not issue replacements for broken or lost CDs (even with a receipt), some online shops will not issue replacement tracks either, so be sure to back up your purchased online music before attempting to edit or convert the tracks. If you throw away your original songs, this is equivalent to throwing away store bought CDs after making compilations from them.