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 combine Zuhr and Asr prayers for being occupied with a wedding ceremony?
No, it isn`t permissible to combine Zuhr and Asr, or Maghrib and Isha because of being busy with a wedding since the exemption for combining prayers is based on lawful excuses, and this isn`t one of them. And Allah Knows Best.
Is supplicating in Qunoot, at times of affliction, during obligatory and voluntary prayer a Sunnah, and should it be done before Rukoo` (bowing), or after it?
At times of affliction, it is a Sunnah that Muslims supplicate in Qunoot after the final Rukoo` of each obligatory, or voluntary prayer as individuals, or in congregation.
Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?
Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.