Is it permissible to perform Qiyam al-Layl half an hour or an hour before Fajr prayer, and does sleeping after Qiyam al-Layl affect the reward?

Qiyam al-Layl (night vigil prayer) is permissible any time before Fajr prayer, and it concludes with the break of dawn. If someone sleeps after performing Qiyam al-Layl, their reward is not diminished, nor is their act of worship invalidated. Indeed, David (peace be upon him) used to sleep after Qiyam al-Layl, and his prayer was the most beloved prayer to Allah. The Prophet Muhammad (peace be upon him) also did so; he used to sleep after his tahajjud (late-night prayer), then wake up for prayer without a new ablution. This is for the purpose of being gentle with oneself and renewing energy to face the day.