Arlington

Thanks for the question. The first thing that I would say is that you should consider having them get their drivers license beforehand.

If you have proof that the car was supposed to be changed three years ago, you should be able to get some kind of compensation. Ultimately, it is up to the insurance company on how they handle billing and policy disputes.

If you have two addresses you would need to list the address where the car is kept most of the time. This is called the garaging address.

Because the damage is minor, it's probably best not to involve your mom's car insurance company. I would recommend having the at-fault party get an estimate for the damage (which they would have to do anyway) and pay for the damage out of pocket.

It sounds like you are fairly confident that the drone was your neighbor's, so in this case you would need to file the damage claim with your neighbor's homeowners insurance company. If there was any dispute as to who was actually responsible, you could file the claim with your auto insurance company (assuming you have comprehensive and collision coverage) to get the repairs started sooner and then it would be handled between your auto provider and the other party's home insurance company.

Yes — you can purchase auto insurance when you don't own a car. This is referred to as a non-owners policy.