Is it permissible for a high school female student to attend mixed-gender private physics lessons (boys and girls) due to the unavailability of a non-mixed alternative, especially since her father refuses for her to go to a distant place? And is she considered compelled to do so, or is her personal effort sufficient?

The prevalent mixing (ikhtilat) in educational institutions today is forbidden, and its harms are great. Studying in such an environment is not permissible unless there is a necessity or a severe need, which is not met in your case. Your level of excellence suffices you from this mixed-gender study. Safety lies in avoiding it and seeking another means, such as seeking help from your female teachers or classmates, or striving to convince your father to go to a center free from mixing. "And whoever fears Allah - He will make for him a way out" (Quran 65:2). You will not abandon something for the sake of Allah except that Allah will replace it with something better. There is no harm in studying in a mixed place if there is a clear distinction between boys and girls, such that each group is on a separate side.