What should a person who doubted having missed a pillar of prayer do?
All praise be to Allah, The Lord of The Worlds. The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah Knows Best.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
What is the ruling on one who feels drops of urine falling during ablution?
If he is certain that urine is exiting from him during ablution, then his ablution is invalidated. He must remove the impurity from his clothes and body and repeat the ablution.
However, if what he feels regarding urine exiting is merely doubt or illusion, then ablution is not invalidated by doubt and illusion. He should not pay attention to it, and it is not permissible for him to follow the doubt and whispers that corrupt his religion. And Allah the almighty 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.