Can I reenter U.S. with H4 visa, and then resume my employment-based I-485 adjustment?

If you are reentering the United States in H1B or H4 Status it doesn't matter that you travelled with an expired Advance Parole document. See...

Can I apply regular Advance Parole (not humanitarian AP) from outside of U.S. while my current AP is expired?

The short answer is "no". Advance Parole is a benefit available to Applicants for Adjustment of Status while their applications for permanent...

The quick answer is "most likely not". The question is whether this unpaid debt could somehow render you inadmissable because somehow it could...