Is Iddah (waiting period) incumbent on an old woman whose husband had died?
Upon the death of the husband, Iddah is incumbent on the wife regardless of their age. 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 the big brother to force his sisters to wear Hijjab (Islamic wear) if their father didn`t do his part in this regard ?
All Perfect Praise is due to Allah, The Lord of The Worlds
The father`s attention should be drawn gently and politely, and the sisters should also be reminded with good words since Allah, The Almighty, Says (What means): "O ye who believe! Save yourselves and your families from a Fire whose fuel is Men and Stones." [Al-Tahreem/6]. And Allah Knows Best.
Is it permissible for a Muslim to escort his deceased disbelieving relative to his final resting place?
It is permissible provided that he doesn`t walk behind non-Islamic symbols, rather he should walk in front of them.