Simplest way would be to automatically email the customer a link with a long randomly generated number (only valid once) when they purchase, when you hit that URL it prompts you to set a username and password.
I have no idea, not an iOS developer. I assume there must be some API or email proxy that you can use to contact customers if they don't reveal the actual address.
I don't think there is a way to get any details at all about a specific purchase on the app store except when using in app purchases.
When using in app purchases you will get a receipt from apple that is signed with their certificate that you can process and send to your own servers to limit pirates from accessing the servers.
