Yes the marriage will be recognized as valid as long as you satisfy the requirements for getting married in the county and state where you plan to marry.
I do not see why they can get married in the U.S. Whether or not it will be recognized by their respective embassies and countries will depend on the laws of their respective countries.
Yes, however the law varies from state to state, and perhaps by city/county as well. You may want to check the eligibility requirements at the local marriage bureau where you seek a license.
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