Does the ruling on shunning a Muslim sibling apply to shunning a female classmate with whom it is not permissible to speak in the first place? And is it obligatory to seek her forgiveness, or is one exempt from that?

The intermingling of young men and women in educational institutions is objectionable. One must lower the gaze, avoid seclusion (khalwa) and suspicious mixing, and refrain from unnecessary speech. It is not permissible to be lenient in these matters under the pretext of friendship or companionship, because it violates Islamic law. Scholars have explicitly stated that it is not permissible for a young woman to speak with non-mahram men without necessity, not even to merely extend a greeting of peace (salaam). Some even prohibited her from returning the greeting of peace to a non-mahram man if he greets her.