Assalaamu alaykum, I would like to know what is authentically established in the books of Islamic history regarding the two major events (i.e. the digging of the zamzam well and the incident of the elephants) in the life of Abdul-Muttalib, the grandfather of the prophet (pbuh), specifically the narration in Dalaa'ilun-Nubuwwah by Al-Bayhaqi on the authority of ‘Ali, may Allaah be pleased with him, wherein he states in detail how Abdul-Muttalib was inspired to dig the well. May Allaah reward you.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.

With regard to the incident of digging the well of Zamzam, which was reported by Al-Bayhaqi in Dalaa’il An-Nubuwwah and was narrated by ‘Ali then the prominent scholar Hammoud ibn ‘Abdullaah At-Tuwaijri classified its chain of narration as good in his book Ar-Ru’yah, as he said after mentioning the incident, “All the men of the chain of narrators who narrated the hadeeth are trustworthy. Ibn Is-haaq narrated his hearing (from his shaykh [teacher]) and this removes the fear of his tadlees (i.e. a narrator reporting a narration from someone as if he heard it directly while in reality he did not) in this hadeeth. Al-Bayhaqi reported it in Dalaa’il An-Nubuwwah from Ibn Is-haaq and its chain of narration is hasan (good).”

As regards the incident of the Elephant, then a Soorah (Chapter) of the Quran was revealed about it, which is Soorah Al-Feel [Quran 105]

It is incumbent upon every person who reads or hears this Soorah to believe in it as a whole; as regards some of its details, then the scholars may differ in confirming them. What was reported about this story with an authentic chain of narrators is what Al-Haakim reported in Al-Mustadrak, and Ath-Thahabi agreed with him; that Ibn ‘Abbaas said, “The people of the Elephant came until they got close to Makkah, and ‘Abdul Muttalib confronted them and said to their commander (leader), 'What brought you to us, master; why did you not send to us and we would bring you everything that you want?' He said, 'I heard that none enters this House except that he feels safe, so I came to frighten its people.' ‘Abdul Muttalib said to him, 'We will give you everything you want, just go back. But the leader refused to leave until he would enter it, and he started moving towards the House, so ‘Abdul Muttalib resorted to a mountain and said, “I will not witness the destruction of this House and its people.'  and then he chanted lines of poetry in which he asked Allaah to protect the Ka'bah. Then something like a cloud came from the direction of the sea until they were shadowed by birds in flocks, about which Allaah says (what means): {Striking them with stones of hard clay} [Quran 105:4], and he said that the elephant started to yell, {And He made them like eaten straw.} [Quran 105:5]

The story is very famous; it is reported in the books of the Sunnah, books of biography, and books of Tafseer (interpretation of the Quran).

Allaah knows best.