Is the story mentioned regarding what Iblis did at the birth of the Prophet, peace and blessings be upon him, and the accompanying events, authentic?

This report has no basis except in the books of the Shia, which are full of lies and falsehoods. As for Iblis being veiled from the heavens at the birth of 'Isa, then being completely barred from them at the birth of Muhammad, peace and blessings be upon him, Al-Baghawi mentioned it on the authority of Ibn 'Abbas as his saying, without a chain of narration.

As for his mother seeing a light at his birth, it is authentically reported from him, peace and blessings be upon him, that he said: "My mother saw, when she was pregnant with me, as if a light emanated from her, illuminating the palaces of Busra in the land of Sham."

As for the shaking of Chosroes' palace, the falling of its battlements, and the extinguishing of the fires of Persia, its hadith (definition) is not sound. Al-Dhahabi mentioned it in Tarikh al-Islam and said about it: "A Munkar (denounced) and Ghareeb (strange) hadith," as cited by the author of Al-Lu'lu' al-Maknun regarding famous signs that are not authentic, due to their lack of sound corroboration.

As for the report about the soothsayers and the removal of their knowledge, it is a weak report.

As for the report about Iblis and the devils and the idols falling prostrate on their faces, its hadith is baseless, attributed to Muhammad ibn 'Umar al-Waqidi, who is accused of lying.

As for him, peace and blessings be upon him, when his mother gave birth to him, falling on his hands, raising his head to the sky, refer to the answer to question number (3341).