Apple Care with coverage of theft and lost

How on Earth can I possibly sign into any applications or my Apple ID for that matter especially when the two factor identification is enabled to get all of the necessary information that is required to correctly file a claim on a lost or stolen phone such as the serial number of the lost or stolen phone which I could get from Apple, but the trusted device that facilitates the codes is lost and even when I try to manually look up a receipt, I can't because a similar process exists in Gmail. The next thing is how is it that I am covered for theft and loss when I must pay for it again for a phone that is way behind in modern smart phone technology, and that I already paid an arm and a leg for refurbished phone?