It depends on the type of damage.
The car's insurance would kick in first because YOU gave them permission. Their insurance would pay for whatever is left over.
I've had a similar issue - I was told to make my neighbour personally liable for any damage and subsequently they can make the claim asked the personal liability section of their house insurance. Thus their house insurance settling my claim for damages
If your neighbor is liable through negligence for causing fire damage to your property you could file a claim on the liability portion of your neighbors insurance policy. If he caused the fire intentionally then his insurance company would not pay for damages as criminal acts are not covered.
good way to get hit with an insurance fraud charge
Since it was caused by the vehicle, the vehicle insurance should cover it. Most home owners insurance companies would probably make a claim against the auto insurance company, if they covered it.
Without anything damaged, lost or stolen there is nothing to claim.
It would be an auto claim for the damage to the other and a homeowners claim for the damage to your property. You cannot be liable to yourself, so you cannot claim the property damage on your auto policy.
The tow company is responsible for damage they did to the vehicle, if they claim they didn't do it you have to prove it and make a claim/sue them, otherwise you need to claim it on your insurance.
It just counts on what your insurance clam is.
Yes you can withdraw your claim, but once reported, the damage and the claim filing are still on record.
Call your insurance company and get a claim started.