Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
What should a person who doubted having missed a pillar of prayer do?
All praise be to Allah, The Lord of The Worlds. The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah 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.
My maternal aunt`s son is living abroad; however, both our families have recited Al-Fatehah declaring our engagement. We have been engaged for three months, but the marriage contract wasn`t concluded because he couldn`t come to Jordan since my mother and brothers are abroad. Is it allowed that he sees my picture without Hijab knowing that the marriage contract will be concluded at the first opportunity?
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.
Betrothal is a promise to marry, so your betrothed is a stranger to you and isn`t permitted to look at you even through a picture. Once your marriage contract is concluded, you become husband and wife and he can look at you as much as he wants. Moreover, he may deputize his father to carry out the procedures of the marriage on his behalf. And Allah The Almighty Knows Best.