Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
It was found out that a man divorced his wife for the third time in 2005, but they continued cohabiting as man and wife. However, when they realized that what they were doing was unlawful, they came the Iftaa` Department in 2009 and were told that they can`t be together. What is the position of Sharia on this couple?
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.
Her Iddah* period starts after the third divorce. As for the continued cohabitation, it is unlawful because being ignorant about the rulings of Sharia while in Dar Al-Islam* is no valid excuse. If a baby came as the fruit of this unlawful consummation of marriage, then a judge of Sharia has the final say in this regard because lineage is a serious matter. And Allah The Almighty Knows Best.
* ʿIddah: a specified period of time that must elapse before a Muslim widow or divorcee may legitimately remarry. The Qurʾān (Sura,2/verse,228) prescribes that a menstruating woman have three monthly periods before contracting a new marriage; the required delay for a nonmenstruating woman is three lunar months.
* Dar Al-Islam: designates a territory where Muslims are free to practice their religion, though this often implies the implementation of Islamic law, whereas Dar al-Harb represents those lands ruled by non-believers
Is it permissible to offer one Rak`ah in Witr prayer?
The minimum of Witr (An odd number prayer performed between Isha`a and Fajr) prayer is one Rak`ah, and the maximum is eleven, but the minimum of its complete form is three, and it is permissible to offer one only.
Is it permissible to pay the Zakah to my grandmother who lives alone in a rented accommodation with bad conditions noting she had three sons.
Zakah cannot be given to ascendants (parents and grandparents). It is obligatory for her sons and grandsons to provide for her, and they would be sinful if they fail to do so. And Allah Knows Best.