Yes a USC may remarry and petition for new spouse.

Yes the Fiance may but possibly better to apply for Fiance visa only.

Yes the Fiance may but possibly better to apply for Fiance visa only.

The daughter may visit on a tourist visa.

LPR spousal petitions can take 2-3 years.

Yes this is possible based on information provided.

Yes you may marry and apply for visa after the fact.

You can do a FOIA request to obtain a copy of your file and I94.

You may need to marry oversees and apply for a marriage based case through consular processing if the visitor visa was denied. Consult with an...

Best to discuss with a lawyer who specializes in Mexican immigration.