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 none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
Is it permissible for the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible so long as his Awrah (private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best
What is the ruling of Sharia on a Muslim woman who committed Zina with a Christian and became pregnant as a result?
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.
Abortion is forbidden in Islam as it entails taking the life of a soul unjustly. Rather, it is one of the major sins; however, it is permissible only when there is well-established danger on the mother`s life; in which situation scholars gave priority to her life over that of the foetus, since this is, according to Sharia: "The lesser of two evils". In case a Muslim woman committed Zina (Adultery) with a Christian and got pregnant, if this did happen, then this question should be presented to the Iftaa` Committee with the presence of the questioner herself. She could also ask a reliable scholar face to face or via phone. If she gives birth to the baby, then he/she is a Muslim and takes the name of his mother; not the name of the man who was a reason for its conception. And Allah The Almighty Knows Best.
Is it permissible to fast on behalf of the dead who died owing missed fast to make up?
His relative should fast on his behalf, and it is permissible for the guardians to give permission to non-relatives of the dead to fast on his behalf as well. And Allah Knows Best.