Is it permissible for a woman who cannot read from the Mushaf to write verses of the Quran on the kitchen walls (ceramic) in order to read from them and memorize, and is it permissible for her to touch printed papers containing verses without being in a state of ritual purity?

It is permissible to write the Qur’an temporarily on a wall for the mother to review and memorize, but it is better to use a whiteboard for that purpose. One must ensure the correct pronunciation of the words before reviewing them from unvoweled writing. Touching a portion of the Mushaf (copy of the Qur'an) without wudu' (ablution) is not prohibited for the teacher and the student during instruction. Maliki jurists have permitted a student to touch the entire Mushaf without wudu', even if she is menstruating. If it is possible to touch it with a barrier or while in a state of purity, that is preferable.