Does QB file and pay my state taxes automatically and electronically? Or do I need to get that set up?

Without knowing your subscription model and what that entails, in addition to what state you are in it is impossible to give you an answer to your question. Too many variables. For instance, your version may include auto pay and file to states but your state might not participate with Intuit, or with the feds,  It seems a simple thing but the IRS does not share your W2, or 1099 with the states.