Q 3:
Ayat-ul-Kursy (the Qur’anic Verse of Allah’s Chair, Surah Al-Baqarah, 2:255) is the best Ayah in the Book of Allah.
It is equivalent to reciting one quarter of the Qur'an, and whoever recites it after each Salah (Prayer) will be admitted to Jannah (Paradise).
A:
Muslim reported in his Sahih on the authority of
Ubay ibn Ka`b (may Allah be pleased with him) that the Messenger of Allah (peace be upon him) said:
'O
Abu Al-Mundhir, do you know which Ayah in the Book of Allah you have (memorized) is the greatest?' I said, 'Allah and His Messenger know best.' The Prophet (peace be upon him) said, 'O (Part No. 3; Page No. 137)
Abu Al-Mundhir, do you know which Ayah in the Book of Allah you have is the greatest?' I said,
Allâh! Lâ ilâha illa Huwa (none has the right to be worshipped but He), Al-Hayyul-Qayyum (the Ever Living, the One Who sustains and protects all that exists).
Upon that, the Prophet (peace be upon him) patted me in the chest and said, 'Rejoice by this knowledge, O
Abu Al-Mundhir!'
Also, the Hadith reported by
Al-Nasa'y,
Al-Tabarany,
Al-Diya' Al-Maqdisy in his collection "Al-Ahadith Al-Mukhtarah", and others scholars, and ranked as Sahih (authentic) by a group of scholars, on the authority of
Abu Umamah (may Allah be pleased with him), that the Messenger of Allah (peace be upon him) stated:
Anyone who recites Ayat-ul-Kursy after each obligatory Salah will have nothing to prevent him from entering Paradise except death.
As for Ayat-ul-Kursy being equivalent to one quarter of the Qur'an in reward, we know of no legal evidence for this.