iMessage secure iPhone

iMessages (as opposed to SMS) are not billed directly by your carrier. They are either part of your data allowance and lumped in with everything else you do that uses data such as sending and receiveing email, web browsing, downloading things or if you're using WiFi, you're carriers not involved at all. They do not appear on your cellular bill.

If someone has an iOS device and has your AppleID and passcode, they could set up their device with it and get your messages. If they have physical access to your phone and it is not passcode protected, they could see your messages.

Does Apple keep some sort of record of your messages? I have no idea. If they do, I suspect the only way to get a hold of it would be with a subpoena.

Best of luck.