I want to update to the most recent firmware while jailbroken
OK, I'll try to answer one-by-one.
Updating without loosing jailbreak
I'm afraid that it's no longer possible. The most recent iOS version - 6.1.3 - does not currently have a jailbreak available. You would keep all you info, but wouldn't keep your jailbreak - nor be able to get it back soon.
Verify this update with Apple
It just means that Apple will sign your update and get stats on what kind of devices are updating, etc. Ever wondered where those percentages they get for the Keynote graphs are coming from? Now you know.
They won't tell AT&amp;T. Even if they did, there is nothing wrong with using a phone without a data plan. Who cares, anyway?
The Backup
Yes, it's only information - apps, app data, settings, pictures, etc.
Restoring to that backup would keep your data and put you on iOS 6.1.3.