As a national, will I still owe state taxes?
Our understanding is that state taxes follow the requirement to pay federal tax. Since you are a national (aka a non-resident alien), you are not required to pay federal taxes, so you would not be required to pay state income taxes.
It is required that you send a notice of your affidavit of citizenship evidence to your state's revenue agency.
Also, you must follow the steps in the Remedy section, IRS, before you stop filing with the IRS.

