Is it permissible for a girl to travel a distance of 500 kilometers and stay for three days accompanied by her female friends and male university colleagues who are not her mahram, without a mahram due to his unavailability, knowing that it is a university trip?

It is not permissible for a woman to travel without a mahram unless there is an extreme necessity, such as migrating from a land of disbelief (dar al-kufr) to a land of Islam (dar al-Islam). Therefore, it is not permissible for your fiancée to travel without a mahram for the aforementioned purpose, especially since such trips may involve corrupting influences and expose women to temptation.