I be wondering if someone near a tourist visa buy a house surrounded by the United States?

The transaction would be paid cash, so there would be no obligation for financing from a bank or nothing like that.
Answers:   
Yes.
Yes, but if you were found and deported you would lose your property.
Anyone can buy and nouns property. There is no immigration law in regards to any owning property OR borrowing money. I would think they would be more likely to pay currency, it's a lot easier.

Many rich retirees from Canada own property in Florida and visit every winter. So tons do this that they even have a name for it. (snowbirds).

On a tourist visa you can't work, you can't get compensated, and you can't stay longer than authorized. You can buy whatever you want.
What is your question?


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