Is what was uttered by the girl considered a vow, and is she obligated to fulfill it or pay expiation for it, taking into account that she promised Allah to abstain from all sins and to comply with all commands?

A promise is not a vow (nadhr), but performing acts of obedience and abandoning sins are religious obligations. If a slip occurs, the Muslim must repent, and there is no expiation (kaffarah) due from him. As for mixed-gender education, it must be abandoned if it involves anything forbidden. To overcome fear, one must think well of Allah and turn to Him, while it is also essential for the believer to be between fear and hope.