1: yes, if you legally export it and get the right paperwork. Which for cars you need anway. Practically you will loose some of the VAT for a refund company, OR spend a lot of time processing it - it is a lot easier with an export business set up.
2: Yes, because it is about the export of the car. But note that you will have to then REIMPORT the car into germany if you - i think, that may be wrong - have the car regularly parked in germany for more than half a year or something. Cars must be registered where they are regularly parked, particularly when you are not in a border crossing situation (i.e. living in germany, working in austria and going back and forth every day). Exporting the car to North Africa and then "using" it in the EU will create for you a TON of legal problems in the long term (as in: you can do so coming to europe as tourist and driving around for 2 months, then returning, but not living) not alone legally (car checks, insurance). Also: You do not think this through - you ask whether you can claim VAT as german citizen in general. Clearly you can, otherwise you could not operate any export business. What matters is that the CAR leaves germany (EU) as legal export (legal because yes, you need the paperwork), not where you reside. There are TONS of businesses that export VAT free, out of the EU. You may have heard that Germany is one of the top exporters in the world - guess what, most exports are VAT free, with the VAT euivalent charged on the import side in the other country.
3: google? Local tax office. Specialized lawyers. Start google with "mwst bei auto export" - and yes, you will need to use german terms here.
Now, practically you may want to talk to a car export company and make a deal with them and pay them some hundred euro for handling the export - and the VAT part. You likely will need a shipping company involved anyway - cars are sort of a little clumsy to handle as cabin luggage on a plane. You can start, i.e. (and I am not realted to) http://www.automarkt-kiefer.com/export.html. Note that pracitally you will have to "pay" VAT and will get it back at some point - no way around it as noone will trust you without being way established and noone wants the liability.