How should the udhiyah be distributed?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to give the poor a portion of the meat from a voluntary sacrifice (Udhiyah al-Tatawwu’), which should not be less than approximately half a kilogram of raw meat. Other parts do not suffice for this obligation, such as the liver, tripe, or intestines.
It is Sunnah for the one offering the sacrifice to divide it into thirds: one-third for himself and his household to eat, one-third to be given as charity to the poor, and one-third to be given as a gift to friends and neighbors, even if they are wealthy. And Allah the Almighty knows best.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
If someone delays making up fasts for a year, can they give fidyah before performing qada?
Yes, it is permissible to give fidyah before making up the missed fasts (qada), because each is an independent obligation, and there is no required order between them.
Is it permissible for the mother to give her children from the Zakah (obligatory charity) of her money?
It is permissible for the mother to give her children from the Zakah of her money if they are Zakah-eligible recipients, and she isn`t obliged to provide for them.