Yes to both, there are no restrictions on the use of a TIN provided for work purposes only. It simply means the poor sap is not allowed to participate in our Social Security System.
It would be reasonable to assume the fact that the borrower is not a U.S. person would be a factor in underwriting the loan, but you can certainly make it if you want to.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.