Is it permissible to memorize the Qur’an with the intention of leading prayers and delivering sermons, while striving to purify one’s intention, and is it permissible to wish to lead prayers in the Sacred Mosque (Masjid al-Haram)?

There is no harm in memorizing the Qur’an for the purpose of seeking to lead prayers (Imamah) and deliver sermons (Khutabah), if the intention is to attain the reward for these acts. These are acts of obedience for those who purify their intention therein. The noble verse: "And make us leaders for the righteous" (Qur’an 25:74) indicates the permissibility of seeking religious leadership, just as some Companions, like Uthman ibn Abi al-As (may Allah be pleased with him), sought Imamah. This is not from the disliked worldly pursuit of leadership, and there is no harm in desiring to lead prayers in the Sacred Mosque, as long as the motive is not the desire for fame and prominence.