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.
Do the Jinn have anything to do with the disappearance of objects?
Jinn are one of Allah creatures, and whosoever lost anything should look for it and never accuse niether the Jinn nor humans of stealing it. And Allah Knows Best.
Is it permissible for a man to lie to his wife? Is it permissible for a man to abandon his wife to work in Saudi Arabia, without her approval, although he is wealthy?
All perfect praise be to Allah, the Lord of the Worlds; may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
The Messenger of Allah commanded men to treat women kindly, so marital problems should be solved through understanding, and whatever causes harm to a woman is forbidden. And Allah The Almighty Knows Best.
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.