Was the Prophet, peace and blessings be upon him, accustomed to turning his face toward the congregants immediately after the salām, or after seeking forgiveness? And when would he recite Ayatul-Kursi and the Mu'awwidhatayn—was it before or after the tasbīh?

The Prophet, peace and blessings be upon him, would seek forgiveness three times after the salutation of the prayer, then turn his face towards the congregants. There is no evidence to suggest a preferred order for the adhkar (remembrances) after prayer, and the matter is flexible. It is legislated after the salam (salutation) of all five daily prayers: seeking forgiveness three times, and saying: "O Allah, You are Peace, and from You is Peace. Blessed are You, O Possessor of Majesty and Honor." Then follow the rest of the narrated adhkar. It is recommended for the Imam to turn his face towards the people after saying: "I seek forgiveness from Allah" three times, and "O Allah, You are Peace, and from You is Peace. Blessed are You, O Possessor of Majesty and Honor." It is also recommended for the worshiper, after each of the five daily prayers, to say SubhanAllah (Glory be to Allah), Alhamdulillah (Praise be to Allah), and Allahu Akbar (Allah is the Greatest) thirty-three times each, and complete the hundred with tahlil (saying "La ilaha illallah" - There is no god but Allah), and to recite Ayat al-Kursi and the Mu'awwidhat (Surahs Al-Ikhlas, Al-Falaq, and An-Nas), repeating the Mu'awwidhat three times after Fajr, Maghrib, and before sleeping.