Is washing both openings (Istinjaa`) a must before every ablution?
Washing the front and back openings (Istinjaa`) is a must in case they have an impurity, but if they do not, there is no need for that, and Istinjaa` is not a condition for the validity of ablution.
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 it permissible for a woman to visit the doctor while in her `Iddah (waiting period)?
It is permissible for her to do that during day time, but it is impermissible for her to leave her house at night except for a sound reason. And Allah Knows Best.
I have asked a marriage official to conclude my marriage since I have no proxy and, being an adult, I can act as the proxy of myself, but he refused. What should I do?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In order for a marriage to be valid there must be a Wali (Guardian) for the woman: father, brother, paternal uncle or any paternal relative. If there isn`t any, then the judge can act as the woman`s guardian and conclude the marriage contract. And Allah The Almighty Knows Best.