What is the ruling on men being examined by a female doctor, and what is the ruling on mixing for the purpose of learning, knowing that the father does not allow abandoning studies?

It is permissible for a woman to study medicine and treat men when there are no male doctors available, provided she maintains her modesty and does not touch or look at what is not necessitated by need. It is preferable for her to specialize in pediatrics or gynecology. Forbidden intermingling is that which leads to unlawful looking or touching, except out of necessity. As for gathering in classrooms for a need, with the woman being veiled and keeping her distance from men, it is permissible.