Is it permissible for a girl to study at a university far from her home for three months?

There is no impediment to a girl attending university, even if it is in another country, provided that she is not exposed to khalwa (unlawful seclusion) or unlawful intermingling with men, and her residence is secure from fitan (trials/temptations) and free from suspicion. It is not a condition for a mahram (unlawful for marriage) to be with her during her stay; a mahram is only required for travel.