Contact USCIS to inquire about rescheduling.

Begin by filing Form I130 on behalf of spouse. Consult with an attorney for guidance.

That would not be enforceable as a subsequent I864 for the AOS was never filed.

Yes expedite requests may be made on the basis of medical needs.

Yes you may travel domestically without issue.

The I-751 interview may be waived depending on the quality of evidence.

Yes you may do so but will need to establish intent to redomicile in the United States.

Yes the answer would be yes given previous filing for your mother.

You may use the Avvo search tool to inquire with an attorney directly.

Yes your valid is still that of permanent resident.