Is it permissible for a financially capable woman to pay the Zakat to her sons or one of them?
It is permissible for a mother to give her children from zakat if they are eligible to receive it, even though she is obligated to provide for them. This is based on the saying of the Prophet Muhammad (PBUH) regarding Zainab, the wife of Abdullah Ibn Mas'ud (may Allah be pleased with them): "Your husband and your children are more deserving of your charity" [Al-Bukhari]. And Allah Knows Best.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
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.
One day, I swore that my wife will be unlawful to me to quit smoking hookah?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
The best course of action is that you turn to Allah for help and quit the hookah. In addition, acquainting yourself with the risks of smoking hookah will help you take this step. And Allah, The Most Exalted Knows Best