What is the ruling on a woman traveling abroad to study with a mahram, with guarantees for her safety and that her religious commitment will not be jeopardized? Is there a sharia prohibition against a woman residing in another country for the purpose of study?

If your stay in the aforementioned country does not pose a risk to your religion, and your father accompanies you on the journey, and you reside in a place where you are safe concerning yourself, your religion, and your honor, then there is no harm in you traveling for study. A mahram is not required during residency, but only for the journey itself, such that he escorts her to her place of residence and then returns or stays with her. Performing Istikhara is good, and it can be repeated; its result will manifest in whether or not facilitation occurs.