My wife filed for Skilled worker (EB-3(A)(i)). Can I apply for NIV to visit her?
There is nothing in law that stops you from getting an NIV. But grant of visas like B-1/B-2 is completely discretionary.
What kind of visa can I get for medical treatment. I have an appointment with a Surgeon in Anderson. Can the visa be extended without leaving America?
Typically, medical treatment in the USA is undertaken on a B-1 ("Business" visa. Strange, huh?). But do not get confused. Consulates often mark visas as B-1/B-2 or even B-2 (visitors/tourist) for medical treatment. Once here, you can ask for extensions of stay if the circumstances so require. I remember extending the stay of a child and his parents for two years (in 6-monthly chunks), where the baby was being treated for ongoing medical problems.