Is staying up late for studying, reciting the Quran, and performing Qiyam al-Layl permissible, provided one is careful to set an alarm or delegate someone to wake them for Fajr prayer, even though this may sometimes lead to missing Fajr prayer until after sunrise, given that this is the best available schedule for the questioner?

It is disliked to sleep before the Isha prayer and to converse after it, unless there is an important need such as studying or revising knowledge. If the prayer is missed due to sleep, there is no sin if you did everything in your power to wake up and intended to perform the prayer on time. Indeed, the Prophet, peace and blessings be upon him, and his Companions, slept through the Fajr prayer and did not wake up until after sunrise, and the pen is lifted from the sleeper until he awakens. However, if you strongly believe you will not wake up, and you can push away sleep until you pray, then you may incur sin by sleeping. One must take measures to wake up, such as setting an alarm and going to bed early, otherwise, you risk incurring sin.