Not entirely true. I believe some municipalities require cars in residential areas to be registered or removed after a certain time limit. So there are local-level laws that can override that statement.
Only if they are in view. Then they can be called an eyesore. But, if it is in your garage, you don't have to register. A number of antique cars are kept in buildings, unregistered. Are race cars registered? I think not.
Firearms are the only consumer product protected by the Constitution, cars are not, so your mixing apples and oranges.