Is it permissible for someone who has not slept at all during the night, such as a student who stayed up late studying, or someone who stayed up until dawn, to perform Ta'ar (waking up for Tahajjud)? Or is it a condition for this that one must wake up suddenly without an alarm?

Summary of the Fatwa:

The noble Hadith that mentions the virtue of one who "wakes up at night" by saying: "There is no god but Allah, alone without partner..." is specific to someone who wakes up from their sleep, whether spontaneously or by an alarm. The Hadith does not include someone who stayed awake all night and did not sleep. The reason for dedicating this reward to one who wakes up from sleep is that in this state, they might have been overcome by heedlessness, and due to the influence of Satan, which is dispelled by this remembrance upon waking. Nevertheless, Allah's bounty is vast, and the answering of supplications and acceptance of prayers are not limited to this remembrance alone.