was wandering whether I am allowed to work unpaid, volunteer unpaid or intern unpaid with a visitor's permit in the US or if I need a visa in order to do so.
You could not do an unpaid internship if it benefits your career. This is considered as you receiving a benefit from the 'work", even though it's not financial benefit. You could volunteer at, for example, a homeless shelter or animal rescue.
The USCIS is generally intolerant of "volunteering" since it could be considered "gainful employment". Generally, a good rule of thumb is that you can volunteer for a religious and/or not-for-profit organization provided it is not the primary purpose of your trip. Providing volunteer services for a for-profit entity is a "no-no". Finally, if you will be uncomfortable disclosing your internship/volunteer services on your next application, then you shouldn't do it.
