Is it permissible to delay Fajr prayer due to insomnia and fatigue from staying up late, especially during school and exam days?

We advise you to organize your time and avoid the causes of insomnia. You are not required to stay awake until dawn; rather, it is permissible to sleep before the prayer time enters, while taking measures to wake up. If sleep overwhelms you and you do not wake up until after the time has expired, despite having taken measures, then there is no sin upon you, and you should pray when you wake up.