Is it permissible to teach the Qur’an to someone who wishes to memorize and interpret it, even though the teacher knows only some of the rules of Tajwid and not all of them, and will he be rewarded for that?

Teaching and spreading knowledge are among the greatest acts of worship. There is no objection to you teaching the girls who desire to learn from what Allah has taught you, and you will be rewarded for that, Allah willing, provided that you do not speak about something whose authenticity you are not sure of, so as to avoid speaking about the religion of Allah without knowledge. Strive to learn and complete your knowledge of the rules of Tajwid and the meanings of the Qur'an. You can seek help from books and websites. If you find someone who has more knowledge than you, sit with her and benefit from her.