Does the hour of answered prayers in the last third of the night coincide with the hour of the Prophet's (peace be upon him) birth and the hour of the gathering of the people of the Diwan in the Cave of Hira, and who are the people of the Diwan and why do they gather in the Cave of Hira?

It has not been established that the Prophet, peace and blessings be upon him, was born in the last third of the night. Rather, he was born on the morning of Monday, the ninth of Rabi' al-Awwal, in the Year of the Elephant. What has been mentioned about his birth at that time and the gathering of the "People of the Diwan" in the Cave of Hira is a myth from the myths of the extremist Sufis. They claim that the Abdal and Aqtāb gather on Laylat al-Qadr (the Night of Power) to distribute provisions and lifespans, and that they have a daily gathering in the last third of the night to determine the affairs of people, speaking in the Syriac language. This is clear disbelief, for Allah alone is the Helper of those who seek help, and seeking help from anyone other than Him is polytheism.