welcome to the Wefugees community and thank you for sharing your question with us!
Buying a car is no problem - private vendors of vintage cars won't even want you to show them your passport as a rule. In case that you receive additional money from the jobcenter, you should ask them up to which amount they would agree with your purchase, i.e. not to charge it as assets.
Registrating a car is a completely different matter. You have to show many documents here, like
- Valid ID (a foreign passport or an ID card)
- Confirmation of registration from the town where you live
- Proof of ownership (part II of the car’s registration certificate)
- Insurance policy
- TÜV-certificate (proof of roadworthiness of the car)
- SEPA debit mandate for payment of vehicle tax
I'd recommend you to get in touch with the vehicle registration office to clarify the dilemmas about point 1, before you buy the car.
I hope my answers were useful for you and I'll be very pleased if you contact me again with further questions. I'm a member of the mbeon-staff and I‘ll be glad to guide over a longer period of time. mbeon is an online advisory service for migrants via the mbeon-app, which you can download on your smartphone for free via Google Play Store (https://play.google.com/store/apps/details?id=de.zone35.mbeon)
or the App Store (https://apps.apple.com/de/app/mbeon-messengerberatung/id1408795643).
You'll find me in the mbeon-app under my name „München, Frau Müller“ and get confidential one-to-one advice in a safe virtual room where nobody can read messages. For more information please visit www.mbeon.de.