Auto insurance is a legal requirement. My insurance company asks me to state where my car is habitually parked, and would consider a misleading answer fraudulent.
Not in all states. In Texas, you do not need auto insurance if you can prove you have the financial ability to pay what an insurance company would otherwise pay.
If you're serious about hiding your physical location, this honestly doesn't seem like much of a showstopper. It happens routinely anyway and, barring obvious red flags, it's going to be hard for an insurance company to discover the fraud.
Not in all states. In Texas, you do not need auto insurance if you can prove you have the financial ability to pay what an insurance company would otherwise pay.