Need car insurance in DE, not a resident..

1. You need a residential address in Germany to register a car. Then you can use that also for the insurance.
2. If you have no residential address, you can only drive a rented car, not own one.
3. If you stay somewhere for longer than a week (or was it two weeks - not sure any more), you MUST register at that address. Registration is possible at AirBnB places and - officially - the host must sign the necessary papers for this. But since many hesitate to do so (and in that case you have no way of forcing them, short of sueing in court), you should make sure of this before booking and select the accommodation accordingly.
4. In most of Germany, public transport (and occasional taxi) is more practical and in many cases cheaper than having a car. If your plan turns out to be too complicated, you could try this! (Car sharing, however, is also only possible with registered address.)

With such uncertainty I would tend towards leasing rather than buying unless one is certain to stay long term. And like Beppi mentioned, one doesn't have to have a permanent address to register. But especially if one doesn't stay in Germany, it would be a lot of trouble to find and buy a car and then have to sell it right away if they leave a few months later. And there are leasing options through both the multiple car-sharing systems as well as all traditional car rental places.

Hello,

Yes, I was actually thinking about this. But would I not have to take out a long term contract to do this, let's say 2-3 years? And if I needed to leave DE after 6 months I am stuck with this leasing contract and must pay it in full? I admit that I don't know a thing about leasing cars. Enlighten me?

Thanks!

Leasing is indeed normally on long-term contracts.
That's why I wrote "rental car" - those are available by the day.