Can a person register a NFA gun in a state they do not live in? Can someone register one in Texas if they live in Alabama? I guess this pertains to legalities both state and federal? What if the person has dual residence or if they don't but have an address for a trust in Texas?

For the most part you should get your trust done under the law of the State you live in. However if you have multiple residences then you can definetly shop around for a more favorable State. Please bear in mind that the firearms must always stay in a State that allows class III ownership.