Distance to the desired car 600km, how best to proceed ?

Hello together, so the following: I found a car, the car is located at 600 km distance. I have no idea of the registration/deregistration/short-term registration I ask for help here because I got to hear various statements in the circle of acquaintances. I would like to test the car and then take it with me immediately. Also I would give my current car in payment (prices have already been discussed, new car is reserved…) How do I go now best before ? I dach and then ? Is there a possibility that the dealer will get me a short-term registration mark in advance, with my authorization and my EVN number of insurance, if I do not take the car I would of course pay for the costs. Is that so usual, can you do it ? Here I can not register him yet because I do not have a vehicle letter, right ? How does that work with the A banmeldung ? Do I have to make that or make that then the dealer without my bite ? Possibility 1: I send the dealer the authorization for the short-term registration mark, and the EVN number of my insurance, then I do the test drive, pay and drive home with the new car and register it here at my place of residence. The seller registers my current “old” car and that was it. Possibility 2: I arrive at the dealer at 9 am, drive together with him to the registration office and We report that car to me, and my old one. Can I then register in another Bundeland directly that car, at best so that I can even keep my old license plate and mount it on the new car? Then drive home with a new car with old license plates. Are there any other “simpleer” options? I look forward to your answers. Thank you very much.