I would be happy to try to answer your questions if you could please be more specific.
Fergus is right (as usual :chuckle -- hey there, girlfriend!) The state Boards of Nursing exist to regulate the practice of nursing within each state and protect the public. There are professional organizations, like the constituent chapters of the ANA (American Nurses Association) and organizations representing the many specialties within nursing, that advocate for nurses, but they typically do not get involved in individual nurses' legal situations. Some nurses in the US belong to collective bargaining units (unions), which represent and support them in lots of different types of "problem" situations, but I don't have any personal experience with that, so I can't say more than that.
Many nurses in the US carry individual professional liability (malpractice) insurance, and many do not. There are several threads on that topic here at allnurses that you could search for and read to find out more about people's opinions and experiences regarding professional liability insurance.
I have worked in both public and private hospitals in the US and am not aware of any difference between them in terms of legal issues for nurses.
If you have specific questions and want to post them here or PM me, I would be happy to try to answer them. There is also a Legal Nurse Consultant forum here, and they may be able to help you with info you are looking for, also.