Another funny thing about US immigration law is, that if you are an international student in the USA (on an F1 visa) you are entitled to work only for the university that has issued you this visa. For everything else, you have to use your OPT (Optional Practical Training), which is a pool of twelve months, that you can use to work for somebody else, while holding an F1. I will not dig into details such as the fact that it costs about $400, and it takes ~ 2 months to apply and be allowed to use a chunk of your OPT.

If you are an international student and not on OPT, you cannot legally work full time/part time/do an internship with the startup your friend just launched (or any other company, on this note). You may want to risk spending your months, or doing some other jazz, and then try to figure things out, but as we can see from the case at hand these maneuvers do not work out well for everybody.

As for sponsorship, from the employer's perspective, the whole visa sponsorship application process costs about $10k, which is not little money for a small company.