Is it permissible for a woman to wait a full day after seeing the dryness to ensure purification from menstruation, especially if she does not see the white discharge and on the same day blood or a brownish discharge might appear? And what is the ruling on a female student being absent from school under the pretext of "health conditions" to avoid a reduction in grades due to frequent absences?

The fatwa (definition) we adhere to is that whenever a woman sees the sign of purity, by one of its two indications (dryness or the white discharge), she must hasten to perform ghusl (definition) and prayer. If bleeding returns, she is considered a menstruating woman again, as long as it is within the possible duration of menstruation. Some scholars are of the opinion that if a woman sees the sign of purity by dryness during her accustomed period, she should wait a day or half a day to ensure the purity has occurred. This is the chosen view of Ibn Qudamah. If one follows this opinion, there is no harm, but what was mentioned first is more cautious. As for being absent from school with a false excuse, it is a forbidden lie, and one must repent from it.