Is it permissible to take pills to induce menstruation before its due time to facilitate leaving the house and performing prayers without embarrassment or hardship, especially during travel and special occasions?

It is not permissible to take anything that hastens menstruation in order to avoid prayer. Some jurists are of the opinion that the blood discharged due to this is not considered menstruation, and prayer and fasting should not be abandoned on its account.

If there is an incontinence of impurity ( سلس للنجاسة ) and it is difficult to purify clothes, then what is difficult to guard against of impurities is excused. This is the doctrine of the Malikis, and it includes what exits involuntarily, such as urine and pre-seminal fluid (madhy). So, if the impurity occurs most of the time and it is difficult to change clothes, there is no harm in praying with them, as a facilitation.