You will need to reestablish domicile for affidavit of support purposes.

Yes you may apply for a replacement.

You may apply for COS using I539. Consult with an attorney for guidance.

See previously answered answer to question.

Use the USCIS fee calculator to determine correct fee.

You may withdraw the I130 and the I864 affidavit of support.

Yes this is possible and happens frequently.

You can provide a note indicating the marital status.

Yes the LPR mother file for unmarried adult son or daughter.

She must be in status to file for adjustment of status.