Is it permissible for a person to give the Zakah(obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and wasn`t provided for sufficiently by whomever is obliged to provide for her.
Is Zakah(obligatory charity) due on the equipments used in the trading process such as: cars , shops etc..?
No Zakah is due on equipments used in the trading process such as cars and the like.
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.
Is it permissible to divide the Aqeeqah amongst one`s brothers and family?
Giving a portion of the Aqeeqah, even a small one, to the poor and needy is obligatory, and if one`s brothers and family are among the needy then, they are more entitled to it, and this way it is a charity and an observation of kinship ties. However, if they aren`t needy then, it is permissible to give them from the Aqeeqah after giving the poor and needy their share.