Your car is not insured unless you purchase insurance for it.
Yes, you can purchase as many policies as you want.
How many days what? The Buyer's Remorse law does not apply to the purchase of a vehicle if that is what you are talking about.
Insurance is purchased for the car, not the driver. Until the car has been insured it cannot be driven by anyone. Note that most states do allow a short grace period after you purchase a car in which it can be driven without insurance to let you purchase insurance and handle title/registration paperwork. This grace period does not apply to a car that you have either allowed the insurance to lapse or have removed its insurance. If you already have another car insured (which it appears you do) and wish to drive a car that is not currently insured, contact your insurance agent and have them temporarily transfer the policy to the other car.
Zero...Car purchase are not covered under a right of rescission law in most states.
A new car is not insured unless you insured it. You can insure a car before you pick it up, but if you don't it isn't insured.
The car is insured not the driver however many policies have restrictions as to who may drive the insured vehicle.
Read the contract that you signed when you made the purchase
Only if the insured car was at fault.
31 days from date of purchase.
You do. (Also, in many states it's illegal to drive a car which is not insured. Expect a hefty fine as well as damages.)
When you buy a car, you have 30 days to get it insured before it becomes illegal, but you are completely financially responsible for any damage done until you are insured.