Re: Renting my car while abroad
You can leave your car with whomever you so please, and you can add his name to the insurance policy (which won't be affected much if at all, unless he's been a PITA to insurers in the last 5 years) so everyone is covered in any case.
How you will arrange with your friend that they compensate you for them having a car to move about freely, is up to you and your friend. If he's not a good friend and you think you need something official, just don't leave your car with someone that you can't trust enough.
If you park it without plates, you don't have to have any insurance if you don't want to, in case Verbier's post wasn't clear. But if the insurance costs make it worth to cover the car's value, then it might be a good option.
Nothing is fool-proof to a sufficiently talented fool