Can someone please pinpoint me where exactly in the Quran/Hadith does it mention that the Moon was split into two and put back together again?
Narrated 'Abdullah: The moon was split (into two pieces) while we were with the Prophet (ﷺ) in Mina. He said, "Be witnesses." Then a Piece of the moon went towards the mountain. -- Sahih al-Bukhari 3869 (sunnah.com), and likewise Sahih al-Bukhari 3636 (sunnah.com) and Sahih al-Bukhari (sunnah.com) and Sahih Muslim 2800 a (sunnah.com)
Narrated Muhammad bin Jubair bin Mut'im: from his father who said: "The moon was split during the time of the Messenger of Allah (ﷺ) until it became as two sections, one above this mountain and one above that mountain. So they said: 'Muhammad has cast a spell upon us.' Some of them said: 'If he could cast a spell upon us, he can not cast a spell upon all of the people.'" -- Jami' at-Tirmidhi, Chapters on Tafsir [grade: sahih] (sunnah.com)
So there's testimony from multiple companions of the Prophet that the moon indeed split in two.