Is a person sinful for being in a mixed-gender university while trying to avoid mixed-gender environments as much as possible? And is a woman's work as a doctor rewarded like a man's?

If the female questioner is able to study at a co-educational university without temptation (fitna) and while adhering to Islamic guidelines, then there is no objection for her. Learning medicine is a communal obligation (fard kifaya) for both men and women to meet the needs of the Ummah. However, if this leads to mixing that causes temptation, then it is not permissible, because preserving one's honor (which is an individual obligation - fard ayn) takes precedence over learning medicine (which is a communal obligation). Mere conversation with a patient or teacher is not forbidden; what is forbidden is speaking in a soft and alluring manner (khudu' bil-qawl). A woman will receive a great reward if she purifies her intention and aims to suffice Muslim women and fulfill this communal obligation.