He cannot just kick you out if you have been living there for longer than 30 days. He can only evict you through Housing Court. Also you may want to contest the will.
You would be well-served to discuss your dilemma with a New York estates attorney in a confidential forum as soon as possible.
You should speak to your attorney about this situation (if you had one). If not, then you will be well-served speaking with a New York litigation attorney and retaining him/her to review/analyze the frivolous nature of his case(s) and come up with a gameplan to reclaim the fees.
It is not illegal if you are staying voluntarily. Feel free to leave if work conditions become unbearable. There are laws governing unpaid internships, however it seems as if you never came to a full agreement on what your position entailed and whether it actually qualifies as an "internship."