Is it permissible for a man to wear transparent clothing?
It is not permissible for a man to wear transparent clothing that reveals his 'Awrah (the area that must be covered). The 'Awrah of a man is "from his navel to his knees", and modesty is more prudent. And Allah 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.
What is the expiation for perjury?
Perjury is forbidden and one of the major sins that require turning to Allah in repentance, seeking His forgiveness, giving back rights to whom they belong, or seeking their forgiveness, and expiating for that oath.
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.