I have a brother who is harsh in his dealings [with me], and many problems have occurred between us, and I do not intend to reconcile with him. What is the ruling of Islamic Law on that?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is not permissible for a Muslim to abandon or boycott his fellow Muslim brother for more than three days. This is based on the saying of the Messenger of Allah, peace and blessings be upon him: "It is not lawful for a Muslim to forsake his brother for more than three [days], meeting each other but one turns away and the other turns away, and the better of the two is the one who initiates the greeting (salam)." (Reported by al-Bukhari.)
A Muslim must strive to end such estrangement (hajr), so as not to fall under the prohibition mentioned in the hadith. If he takes the initiative to reconcile but the other party does not respond, then there is no sin upon him. We remind [ourselves] of the saying of Allah, the Exalted: "And let them pardon and overlook. Do you not wish that Allah should forgive you? And Allah is Forgiving and Merciful." (An-Nur/22). And Allah, the Exalted, knows best.
What should one who doubts the validity of his ablution and performs it frequently do?
Whoever doubts the validity of his ablution after finishing it, his ablution is valid. This is because the default is the validity of the ablution, and because doubt after finishing an act of worship doesn`t affect its validity. And Allah the Almighty knows best.
How many Rak`ahs (unit of prayer) are offered in Witr prayer?
All perfect praise be to Allah, The Lord of The Worlds Witr (an odd number prayer performed between Isha`a and Fajr) is offered with a minimum of one Rak`ah, and a maximum of eleven, but offering three Rak`ahs is the minimum of its complete form. And Allah Knows Best.
Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?
Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. And Allah Knows Best.