Does praying seven rak'ahs before Fajr, in addition to the other mentioned supererogatory prayers, fulfill the sound Sunnah and suffice for the Shafa' and Tahajjud prayers?

"Shifa'" (Even) refers to two, six, or eight rak'ahs. "Witr" (Odd) refers to one, three, five, seven, or nine rak'ahs. "Tahajjud" is the night vigil prayer performed specifically after sleeping. You can intend seven rak'ahs for Tahajjud and Witr, and this includes the "Shifa'". Praying two rak'ahs after 'Isha, two rak'ahs before 'Asr, and two rak'ahs before and two after Dhuhr, in addition to four rak'ahs of Duha prayer (two by two), are among the established Sunnah prayers.