To what extent are the hadiths mentioned authentic regarding the virtue of learning the Qur’an, teaching it, reciting it, and memorizing it, and the virtue of those who do so, and the virtue of the parents and the teacher?

Summary of the specialists' stance on the mentioned Hadiths and narrations:

1. "Three people do not care about the reckoning": This is a fabricated (Mawdu') Hadith in this context. 2. "Whoever kisses his child, Allah writes a good deed for him": Not found. 3. "Indeed, this Quran is Allah's banquet": Weak when attributed to the Prophet (Marfu'), but authentic when attributed to Ibn Mas'ud (Mawquf). 4. "There is no believing man or woman...": Al-Qurtubi mentioned it with a form of weakening (reported), and it was not found in the books of Sunnah. 5. "The best among you is he who learns the Quran and teaches it": Authentic. 6. "The teacher of the Quran and its learner...": Not found with this wording. The correct wording is: "And indeed, the learned one is sought forgiveness for by all those in the heavens..." 7. "Learn the Quran, for the one who carries the Quran is like a man who carries a satchel full of musk": Not found with this wording. Similar wordings have been reported, which Al-Tirmidhi deemed good (Hasan) and Al-Albani deemed weak (Da'if). 8. "Whoever teaches his child the Quran, it is as if he performed Hajj ten thousand times": Not found. 9. "There is no man who teaches his child the Quran...": Denounced (Munkar) and weak (Da'if). 10. "The best among you is he who learns the Quran": Authentic. 11. The narration of Ali (may Allah be pleased with him): "And learn the Quran, for it is the best speech": Mentioned in a sermon by Ali (may Allah be pleased with him), and has connected corroborating evidence. 12. "If a teacher says to a child...": Fabricated (Mawdu'). 13. The saying of Abu Abdillah: "A believer should not die...": Not found. 14. "Illuminate your homes...": Not found with this wording. Similar wordings have been reported, which are weak (Da'if). 15. "Three will be on dunes of musk...": Similar wordings have been reported, which are weak (Da'if). 16. "Indeed, this Quran is the rope of Allah": Reported with various and similar wordings, which are weak (Da'if). 17. "O Salman, adhere to reciting the Quran": Not found. 18. "You must recite the Quran and remember Allah": Authentic. 19. "Indeed, the parents of the reciter will be crowned...": Not found with the mentioned wording. Parts of it have been reported in authentic Hadiths with similar wordings. 20. "Indeed, hearts rust...": Weak (Da'if).

Note: What is in Nahj al-Balagha has not been authentically attributed to Ali (may Allah be pleased with him).