Is it permissible to delay the ritual purification (ghusl) from major impurity (janabah) until after dawn?
Yes, it is permissible to delay ghusl from janabah until after dawn, as purity from janabah is not a condition for the validity of fasting. However, one must perform ghusl in time to pray Fajr within its designated time.
Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.
Is it permissible for a woman to give the ransom (Fidyah) for breaking her fast to her granddaughter (her son`s daughter)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for a woman to give the ransom (Fidya) for breaking her fast in Ramadan to her granddaughter (her son’s daughter), provided that the girl is poor and her basic needs are not being met by the maintenance (Nafaqah) of those who are lislamically obligated to provide for her. And Allah the Exalted knows best.
Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.