Is it permissible to make ablution without answering the call of nature after waking up?
Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najaasah (impurity), thus if there is no Najaasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature. However, prayer is invalidated if there is Najaasah on the anus ,or the front opening, so it (Najaasah) must be removed for the prayer to become valid, and not the ablution.
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.
Is it permissible to give the expiation due on the vow of anger to one person?
The expiation for the vow of anger-and that of the oath-is to be given to (10) needy persons, or a needy family of ten individuals, but giving it to one person is impermissible.
A man cursed Allah, is he allowed to perform prayer without making Ghusl?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Cursing Allah is an act of apostasy and one who commits it must utter the testimonies of faith, make repentance, take back wife; however, it isn`t conditioned that he makes Ghusl (Full body ritual purification) to pray. And Allah The Almighty Knows Best.