Does the reward for the night vigil (Qiyam al-Layl) increase for one who sleeps and then wakes up for it, compared to one who does not sleep at all during that night for it? And does the reward decrease for one who deliberately stays awake until morning for it?

Performing Qiyam al-Layl (night vigil prayer) after sleep is the best type of supererogatory prayer. It is stated in Tafsir al-Qurtubi that Tahajjud is waking up after a period of sleep, and this was also the prayer of the Messenger of Allah, peace and blessings be upon him. And whoever intentionally wakes up and performs Qiyam al-Layl in its last part without having slept, he will attain the reward of Qiyam al-Layl, in addition to the reward for his intention and his eagerness not to miss this great act of worship.