The answer to your questions is; maybe. The issue is really; where will you get the home loan and will the bank know that you are not a citizen?
I am not aware of any law which would preclude you from purchasing a home in the US while on a visitor visa. Having said that, even though you have the ability to purchase the home in the US, why would you purchase a home in the US without a guarantee that you can obtain another visa?
With regard to the home loan, it is likely that a lender will not want to loan you money if they know that you are on a visitor visa, soon to expire.
I hope this helps.