What is your advice to university girls who compete in not wearing the hijab, or wearing an un-Islamic hijab, and who talk to young men without restriction, and travel with them without a mahram? What is the ruling if their guardians encourage this for the purpose of marriage?

The hijab is obligatory for Muslim women, and it is not considered a legitimate (shar'i) hijab unless certain specifications are met. It is forbidden for a woman to wear makeup or other adornments when going out such that non-mahram men see them, due to the Almighty's saying: "And not display their adornment except that which is apparent of it." The mixing of women with non-mahram men and conversing with them without legitimate (shar'i) controls is forbidden because it is a cause of corruption and temptation. A woman's guardian is responsible for her before Allah the Almighty, and he must protect her and prevent her from causes of corruption. Being lenient with her in this regard is forbidden and constitutes a form of "dayatha" (cuckoldry/lack of protective jealousy).