Yes they can ..
Although it would not effect their rights to marridge, they would risk deportation unless marrying citizens of the US, and so it is not advisable.
Oman is friendly to the US.
Yes, it can be. You need to bring copies of your marriage certificate and license to file with your state and county recorder. Otherwise your marriage may not be recognized in all cases.
Oman is mainly a British ally.
your butt
There are various reasons that Britain's citizens might immigrate to the US. For example, they might move there to marry an American they met on the internet.
yes, they marry just like tow citizens would in the state of Kentucky, you need a birthcertificate and apicture ID.
yes
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
Yes, if they have the documentation that is required by the state in which they wish to marry.
According to CousinCouples.com, second cousins can marry anywhere in the US.