There are no limits on a non-resident alien opening an LLC or corporation in the US. Opening the company does not provide visa benefits (residency and work permission.)
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
There are no restrictions on who can form and who can own a U.S. company that would conflict with what you want to do.
Having a U.S. company does not require a right to come to the U.S., but does not give you one either.
A company can perform any legal business and do it from anywhere. There may be tax implications of collecting payment in the U.S., but since you will be setting up a U.S. company, withholding at source should not apply.
Yes, you would certainly be able to form a New York LLC. This does not, however, automatically entitle you to obtain a work visa if you plan on operating the business from the United States.
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