What is the reward for reciting Surat An-Naba, Surat Al-Waqi'ah, Surat Ya-Sin, and Surat Al-Mulk, with evidence from the Sunnah, and with which surah should I begin memorizing, and is it permissible to recite the memorized portion in a supererogatory prayer, and what should I do when I make a mistake or forget during recitation?

First, the virtues of the Surahs: - Surah (definition) An-Naba: It has no special virtue except that it is one of the "severely warning surahs" that caused the Prophet (peace be upon him) to gray, and every letter from the Qur'an brings ten good deeds. - Surah Al-Waqi'ah: The hadith (definition) regarding its virtue, that it prevents poverty, is not authentic. - Surah Ya-Sin: All hadiths regarding its virtue, such as it being the "heart of the Qur'an," or reciting it ten times, or reciting it over the deceased, or lightening the torment for the people of the graves, are not authentic. - Surah Al-Mulk: Authentic hadiths have been reported regarding its virtue, stating that it intercedes for its reciter until he is forgiven, and that the Prophet (peace be upon him) would not sleep until he had recited it.

Second, methods of memorizing the Qur'an: Memorization methods vary from person to person, and one can start with easy and frequently heard surahs. To solidify memorization, constant repetition and acting upon the verses are essential, as is reviewing during prayers, especially the night vigil (Qiyam (definition) al-Layl). If you forget something during prayer, try to recall it; if you cannot, then skip the verse and review it after the prayer.