Here's what the USCIS website says about refunds:
When you send a payment, you agree to pay for a government service.
Filing and biometric service fees are final and non-refundable,
regardless of any action we take on your application, petition, or
request, or if you withdraw your request. Please refer to the form you
filed for additional information, or ...
Your parents can file AOS (I-485). The lawyer is wrong, but the USCIS person you spoke to is not entirely correct either.
What the lawyer may be thinking of is the fact that in most categories, one is barred from Adjustment of Status if one is out of status at the time of filing (See USCIS Policy Manual, Volume 7, Part B, Chapter 3). For the purposes of this ...
What could be the consequences if I apply for the US?
For just applying, there will be no technical consequences as long as your applications is genuine and contains only truthful factual information. But applying so shortly after your previous ban has lapsed will certainly raise some eyebrows. It's just human nature.
Is my ban period done?
You seem to ...