Well, there is no visa specifically to buy property. So the only one that really fits is the B-2 tourist visa. That would allow you to stay in the U.S. for up to 6 months and you can extend it for up to 6 more months for a total of 1 year without having to leave the U.S. As far as how long you would have to leave before coming back, the law only says that in order to “reset” the time given on a B-2 visa, you can go anywhere in the U.S. for one day and come back except Mexico, Canada or any of the adjacent islands to the U.S. If you go to one of those, you would have to go for 30 days or more to “reset” the time. The problem with doing that is that you may get away with it one, or twice, but at some point you need to start spending more time outside of the U.S. than inside of the U.S. That would be the general rule. So if you spend 6 months, you should probably stay out 7 months or more. If you stay 1 year in the U.S., you may want to stay out of the U.S. for 14 months or more. It’s not a specific rule, but a general idea because you cannot give the impression that you are living in the U.S. and just leaving to reset your time. I will provide you with two links that may be helpful. The first is to an article that will explain what they look for when issuing a non-immigrant visa like the B-2. The second is a list of things that can be presented to prove non-immigrant intent and the strong ties to the home country.
As to tax consequences, I am not an accountant and cannot really tell you much about that, but if you are spending more than 183 days in the U.S. out of any year, you would be subject to U.S. taxes. Here is a link:
There may be a tax treaty between the U.S. and the UK to prevent double taxation but you would need to speak to an accountant about that.
As far as selling the property, the tax consequences would most likely be high due to capital gains unless you purchase another property within a certain amount of time after the sale. Again, you would need to speak to an accountant to know more.
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