How are many missed prayers, of unknown number, made up? And should the oldest ones be made up first, or the newer missed prayers that occur due to the nature of work and sleep?

You must fear Allah and perform your Dhuhr and Asr prayers on time, as the claim of not waking up is not realistic. Instruct your family to wake you up, use an alarm clock, and take all necessary measures to wake up; for neglecting prayer is a grave danger. You must also make up all missed prayers.