What is the ruling on a woman traveling to study in a foreign country accompanied by her mother instead of a mahram (unmarriageable kin), and does the hadith apply to her: "If a woman wishes to enter Paradise, she should not travel a day's journey without a mahram"?

It is not permissible for a woman to travel without a mahram, and there are authentic hadiths to that effect. The matter becomes even more serious if the travel is for residence and study in foreign lands. A mother is not a mahram for her daughter. Furthermore, the mixing found in foreign universities prohibits studying in them, even with the presence of a mahram. A woman must fear Allah and study in her own country or via correspondence, if possible.