Is it obligatory for a girl to purify herself, pray, and recite the Quran when her intermittent menstrual bleeding stops, then cease praying when it returns? And is this pattern considered an illness?

"Complete cessation of blood flow" (al-jufūf) means that a woman inserts a piece of cotton and it comes out dry, untainted by blood. If the blood flow stops but the cotton is still stained, then this is not considered a complete cessation. The al-jufūf that lasts for less than a day (i.e., for a few hours) and then the blood returns is not considered a state of purity (ṭahāra). This is the ruling (muftā bihi) according to some scholars, because blood sometimes flows and sometimes stops, and obliging ghusl (definition) (ritual bath) upon someone who becomes pure for an hour after an hour would be an undue hardship, unless the cessation occurs at the end of her usual period or she sees the white discharge (al-qaṣṣah al-bayḍāʾ, a white fluid indicating purity). Based on this, a cessation of a few hours (less than a day) is not considered a state of purity unless it occurs at the end of the menstruation period or she sees the white discharge. Reciting the Qur'an is permissible without directly touching the Mus'haf. As for considering what is happening a medical condition, doctors should be consulted regarding that.