Does touching women temporarily forbidden in marriage nullify ablution?
It is prohibited to touch, or to shake hands with such women as they are considered strangers, and doing so nullifies ablution.
Is it permissible to sleep after the time of the Fajr prayer has begun, with the intention of waking up shortly afterward?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
If a person sleeps after the time of Fajr has begun, with the second adhān, then sleeping is forbidden (ḥarām) at that point, unless he is certain that he will wake up and perform the prayer within its time. And Allah Almighty knows best.
What is the ruling on brown discharge before the menstrual period? Is it considered part of menstruation (Hayd)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Dusky discharge (Kudrah), reddish discharge (Humrah), and yellowish discharge (Sufrah) are all considered menstruation (Hayd) if they occur during the time of the menstrual cycle. If their duration exceeds a day and a night, and the period persists from the first sight of the discharge until the cessation of the menstrual blood—provided the total duration does not exceed fifteen days—then all of it is menstruation. However, if the duration exceeds fifteen days, then the discharge is not considered menstruation, but rather chronic irregular bleeding (Istihadah). And Allah the Exalted knows best.
Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?
It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.