Is it permissible to agree that the mahr be the memorization of three parts of the Holy Quran, and what is the ruling on this agreement and its reward, and will the husband be rewarded for it?

What you did by memorizing the Qur'an in response to your wife's request is a good deed for which you will be rewarded, as the Prophet, peace and blessings be upon him, said: "The best among you is he who learns the Qur'an and teaches it," and "Whoever recites a letter from the Book of Allah will have a good deed thereby." Your wife will also be rewarded for making that request, as he, peace and blessings be upon him, said: "Whoever guides to a good deed will have a reward like that of its doer."