Unless the marriage is contrary to the laws of their U.S. state of residence - the U.S. does generally recognize marriages legally performed in most other countries.
Generally no. You cannot legally marry anyone if you are still married to a different person, regardless of where that marriage was performed.
Mexico US citizens can legally purchase guns from a gun dealer or from another individual. There are a few states that have restrictions, but most do not.
You can legally bring your fiancee from Mexico with a "fiancee Visa" and you will have 3 months to marry him.
A marriage in Mexico by U.S. citizens is not recognized as legal in the U.S. One could marry in both Mexico and in the U.S. without worry of penalty. However, if they are U.S. citizens, only the U.S. marriage would be considered legal.
No. No one is allowed to be married to more than one person at a time in the US or Mexico.
The first thing you should do is ensure that she never becomes an illegal immigrant. If the two of you are ready to marry, she should come to the US legally, with a passport and visa, and marry you here, or you should travel to Mexico legally, with a passport and visa, and marry her there. Either will technically work, but if you are planning to live in the US after you are married, then it would be best and easiest in the long term for the marriage to have taken place legally in the United States. In that case, you should seek a 'Nonimmigrant Visa for a Fiancee' for her (see link below) and then follow the proper procedures to have her become a citizen (see second link below).
If one of the parties is not a US citizen, it may make things easier. They would have to apply for a visa and if they are not in the US legally, it can be difficult.
It can be if you do the right paperwork through the Mexican government and get a blood test there, etc. I got married in Jamaica and it was much easier
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No, in most countries it is illegal (a crime) to marry someone that is still legally married to another person.
Citizens can legally stay forever.
Yes. About one third of us that are adults do own guns. Legally.