by “death” here—Allah knows best—is the death of sleep, for sleep is called wafāh (the taking of the soul). It could also refer to the greater death, the soul’s actual departure from the body, as in His saying: “Say, ‘Indeed my prayer, my sacrifice, my living and my dying are for Allah, Lord of all worlds’” (Q 6:162). When he awoke he would say, “Praise be to Allah who brought us back to life after having caused us to die, and to Him is the resurrection.” This confirms that the “death” in “In Your name, O Allah, I die and I live” means the death of sleep, the lesser death.
As for the report of ʿĀʾishah, she related that the Prophet ﷺ used to pray eleven rakʿahs during the night. That was the most he prayed—either eleven or thirteen—and he might perform fewer than that according to how energetic or tired he felt, may Allah bless him and grant him peace. When dawn broke, he would offer two light rakʿahs—the Sunnah of Fajr. The Sunnah is to keep them brief: in the first rakʿah he would recite “Say, O disbelievers” (Sūrat al-Kāfirūn) and in the second “Say, He is Allah, the One” (Sūrat al-Ikhlāṣ); or, in the first, “Say, ‘We believe in Allah and in what has been revealed to us…’” to the end of the verse (Q 2:136), and in the second, “Say, ‘O People of the Scripture, come to a word that is equitable between us and you’” (Q 3:64). What matters is that he lighten them, shortening the bowing, the prostration, the standing, and the sitting.