What is the authenticity of the hadiths narrated concerning Umar ibn al-Khattab's doubt about the prophethood of the Prophet (peace be upon him), or his adding to the Book of Allah, and what is the clarification and explanation of the phrase "By Allah, I have not doubted since I embraced Islam except on that day"?

The virtue of the Companions is established by the Qur'an, Sunnah, and consensus (ijma'). This includes the virtue of the Muhajirun and Ansar, the people of the Pledge of Ridwan, the Household of the Prophet (Ahl al-Bayt), and the Four Rightly Guided Caliphs. There is also consensus on the uprightness of the Companions, as they were the transmitters of the Sharia.

As for the statement of Umar, may Allah be pleased with him, "By Allah, I have never doubted since I embraced Islam except on that day," this was during the Treaty of Hudaybiyah. It was not a doubt but a request for clarification of what was hidden from him and an urging to humiliate the disbelievers.

Regarding his statement, may Allah be pleased with him, concerning the verse of stoning (rajm): "I would have established it as it was revealed," he did not intend to add to the Qur'an. Rather, he wanted to emphasize that the ruling of stoning for married fornicators is established by the Book of Allah. This verse was recited, then Allah abrogated its recitation while preserving its ruling, which is a type of abrogation permissible legally and rationally.