Is it permissible for a sister to travel to study and reside in a university dormitory in an area approximately 200 km away, knowing that there is no mahram for her in the dormitory?

A woman is not permitted to travel except with a mahram. The questioner or one of his sister's mahrams must accompany her on her journey, both to and from her destination. As for her residence at the university with her female colleagues, there is no harm in it if the accommodation is under secure guardianship and the girls adhere to Islamic manners therein.