Nice to hear from you again!
It's true that you can get a so-called "Ausbildungsduldung" for the duration of your Ausbildung. It enables you to stay in Germany for ~3 years (usually) and after that you will have 6 months to find a job in a related field. If you succeed you will get a residence permit for another 2 years. In addition, your chances on the labour market will be better and you will probably get a better-paid job than at McDonald's. As far as I can see, you need to have a passport or a so-called "Passersatz" (a document that works as a substitute for your passport) in order to start an apprenticeship.
After working for 2 years you are allowed to work in a field that is not connected to the profession that you had your training in. That's what it says in §18a (2) AufenthG. To me that sounds like your residence permit will still be valid (or it will get prolonged) after 2 years.
If I'm wrong and that doesn't work, you can get a residence permit after 8 years of staying in Germany. Please keep in mind the answer provided in this thread:
As long as you fulfil the criteria listed, you should be granted a residence permit after 8 years.