Plainview, TX Immigration Law Firms & Lawyers

You have clearly identified all of the issues. If one likes to exercise an abundance of caution, they'd file for the B-2 extension, but it could also be denied for immigrant intent. On the other hand, I've had the B-2 extension approved in cases exactly like this.

Excellent question.  If you are a U.S. Citizen, you can certainly petition her for a fiancee visa (K-1 visa) and then marry her in the United States.  You would have 90 days to marry her and then you would do an adjustment of status from K-1 to the green card.  You would also request a travel document.   While her green card is pending, she cannot travel outside the United States until she receives an Advance Parole (travel document).  It takes about 90 days to obtain it.   If you marry in Monterrey, Mexico in June, then you would petition her for an immigrant visa and she would consular process out of Ciudad Juarez, Mexico.  She would then enter the U.S. with a green card and if there were any emergencies in Mexico, she could travel immediately because she would have the green card. I hope this helps.  

There is no specific law on that, and as long as they have a visa they can get on a plane to come. It is up to the officer at the port of entry whether to let them in.