What is the distance at which a mahram must be present with a woman during her travel? And is it permissible to travel for study for half an hour on mixed transportation alone?

If the duration of the student's journey to the university is not considered a سفر (travel) by custom, then it is permissible for her to go alone, provided she adheres to the شرعي ( Shar'i) hijab (definition) and Islamic manners. As for the mixing of men and women in transportation, there are two types: First, each man and woman sitting in a separate seat without physical contact, while adhering to the شرعية (Shar'i) manners; there is no harm in this. Second, a man physically touching a woman or mixing without adhering to the شرعية (Shar'i) controls; this is not permissible, and she must seek another means of transportation free from these violations.