Does the worshiper incur responsibility for shortcomings in the conditions of imamate that must be met if he leads the people in prayer while ignorant of some of them, despite the presence of someone better than him in memorization and recitation?

If your recitation of the Quran is free from clear errors (laḥn jalī) that alter the meaning, and you are knowledgeable and observant of the rulings of purification and prayer, then there is no harm in you leading the congregational prayers (imamah), even if there are those among them who are better than you. Scholars have permitted the leading of prayer by someone of lesser merit (mafḍūl) over someone of greater merit (fāḍil). The Prophet, peace and blessings be upon him, prayed behind Abd al-Rahman ibn Awf, and the Companions prayed behind Al-Hajjaj. However, if you have shortcomings in tajwid (recitation) or knowledge of the rulings, then you must strive to learn and improve your level.