Non Resident starting business in US
My question is: If I open a LLC, will I be liable to US regarding tax income? Or my LLC business?
As an LLC is a pass-through entity, the company itself would not be subject to taxation. The income generated by your company would go directly to your personal income, so while you are living in Illinois you would be subject to paying state and federal income tax on your profits.
Once you move out of the United States, you will still be able to own the company, however at the point it would be a very good idea to consult with an accountant familiar with international tax laws regarding how your profits would be taxed.
Keep in mind visas such as F1 come with lots of restrictions, so it is a good idea to consult an immigration attorney on what you as the owner of a company can and can't do in order to maintain your immigration status.
Also something to keep in mind, while an LLC does not pay tax on it's income, Illinois state charges $250 a year to file the company's Annual Report.