Can a young male teach a woman in khalwa (being alone) with her wearing her niqab or sitar? What if there are more people?
No. This is not allowed. Some Scholars say it is not allowed, even if there is more people, because it is a fitnah. There is no need for a man to teach a woman in this situation. She should search for a female teacher. Free Mixing is forbidden. It is allowed to teach her only through a speaker, or if there is a curtain to segregate.