Is it our responsibility to insure a car that we own, but don t drive?

Yes

It is your responsibility to insure any car that you own and someone drives. In some states, you must insure any car you own, even if no one drives it, so you must either pay for insurance or sell the car or gift the car to someone else. In other states, you only need insurance if someone drives the car and you don't need insurance if no one drives it, but you do need insurance if anyone drives it, even if you don't.

You are not forced to pay for insurance. You have two other options: You could sell the car or you could gift it to someone else.

If it has tags on it, then yes. If it parked on private property and no one is driving it, then no.

Yes

yes and even in driveway you can be fined for no insurance