Going between al-Safa and al-Marwah is the practice of Hajar (peace be upon her)

Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrated that he saw the people going between al-Safa and al-Marwah and said: "This is among the things that the mother of Isma'il (peace be upon him) (Sayyidah Hajar) left to you as an inheritance."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Imam Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) concerning the saying of Allah Almighty, "Indeed, al-Safa and al-Marwah are among the symbols of Allah" [Surah al-Baqarah: 158], that he said: In the Jahiliyyah, the devils used to play music the whole night between al-Safa and al-Marwah, and their idols were also placed there. When Islam came, the Muslims said: O Messenger of Allah, we will not go between al-Safa and al-Marwah, for it is something we used to do in the Jahiliyyah. Then Allah Almighty revealed this verse: whoever performs Hajj or Umrah, there is no sin upon him for going between them. That is, it means there is no burden of sin upon him; rather, there is reward for him.
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that he said: Were it not for a verse in the Book of Allah, I would not have told anyone anything. It was asked: O Abu Hurayrah, which verse is it? He replied: "Indeed, those who conceal what We have sent down of clear proofs and guidance after We have made it clear to the people in the Book, it is they whom Allah curses and whom those who curse also curse, except those who repent, make amends and make (the truth) clear" [Surah al-Baqarah: 159-160].

It is narrated from Sayyiduna Ubayy bin Ka'b (may Allah be pleased with him) that he said: Do not revile the wind, for it is from the breath of the Most Merciful (that is, His relief and mercy), as Allah says: "And the directing of the winds and the clouds held between the heaven and the earth" [Surah al-Baqarah: 164]. Rather, supplicate: 'Allahumma inna nas'aluka min khayri hadhihi al-rih, wa khayri ma ursilat bihi, wa na'udhu bika min sharriha wa sharri ma ursilat bihi' (O Allah, we ask You for the good of this wind and the good with which it has been sent, and we seek refuge in You from its evil and the evil with which it has been sent).
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it; and this hadith has also been narrated from Habib bin Abi Thabit through other chains.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) concerning the saying of Allah, "And all their ties will be cut off from them" [Surah al-Baqarah: 166], that he said: (The ties mean) mutual love and affection.
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abu Dharr (may Allah be pleased with him) that he asked the Messenger of Allah (peace and blessings be upon him) about faith, and he recited this verse: "Righteousness is not that you turn your faces towards the East and the West, but righteousness is (in) one who believes in Allah and the Last Day" [Surah al-Baqarah: 177], until he completed the whole verse. He asked again and he recited it again; he asked again and he recited it again. Then he asked him, and he (peace and blessings be upon him) said: "When you do a good deed and your heart loves it, and when you do an evil deed and your heart hates it (then know that you are a believer)."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) concerning the saying of Allah, the Mighty and Majestic, "And gives wealth, despite love for it, to relatives" [Surah al-Baqarah: 177], that he said: (It means that) a man gives wealth in charity while he is healthy and has greed for wealth in his heart, hoping for a long life and fearing poverty and hardship.
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.