Is it permissible for me to start teaching a child the Qur'an and the interpretation of its verses, knowing that I have not yet memorized Juz' 'Amma, and I have already taught him Hadith and stories of the prophets?

It is not permissible for someone who has not received the Qur’an through oral transmission to teach it. This is because there are letters that are pronounced but not written, and letters that are written but not pronounced, in addition to the necessity of knowing how to pronounce correctly, the points of articulation (makharij al-huruf), and the characteristics of the letters (sifat al-huruf). "Do not take the Qur'an from a Mushaf (copy of the Qur'an) nor knowledge from a mere written text." However, there is no objection to teaching a child what you excel at from the Qur’an, whether in recitation or interpretation, even if it is just one surah or one verse, due to the saying of the Prophet, peace and blessings be upon him: "Convey from me, even if it is a single verse," and "The best among you is he who learns the Qur'an and teaches it."