I just started online banking yesterday with my local bank. When you bank online do your paper bank statements automatically become paperless?

Have to ask your bank. Different policy for different banks. I still get a monthly statement by postal mail however..

If you agree to receiving your statements online then the bank will not issue paper ones.

Ask the bank. Each has different policies.

Most banks require that one explicitly consent to/request such.

Absolutely! I think you should get a car loan. Hope this helps!