Are the practices that involve reciting Ayat al-Kursi and Surahs al-Ikhlas, al-Mu'awwidhatayn, and al-Kafirun, and supplicating for forgiveness, entry into Paradise, and safety from punishment and evils, and supplicating for one's parents, and saying Takbir and the two Shahadas before sleep, permissible in Islam?

The remembrances (adhkar) and numbers mentioned by the questioner have not been authentically transmitted in the Sunnah as adhkar for sleep, apart from reciting Ayat al-Kursī, the two Mu'awwidhatayn (Surahs Al-Falaq and An-Nas), Surah Al-Ikhlas, and uttering the Takbir (Allahu Akbar). These are the legislated adhkar for sleep, but not with the numbers mentioned. The best guidance is the guidance of Muhammad, peace and blessings be upon him, and adhering to what has been legislated is all good.