Is it permissible for a person who has to make up for missed fasts to fast six days of Shawwal (the month directly after Ramadan) before making up for the missed fasts?
Yes, it is permissible for him/her to do so, but it is better that they make up for missed fasts first. And Allah Knows Best.
What is the ruling on a woman driving a car?
All Perfect Praise is to Allah, The Lord of The Worlds, and may His Peace and Blessinsg be upn our Prophet Muhammad and upon all of his family and compnions.
It is permissible for the woman to drive a car, but it is impermissible for her to travel unaccompanied by a Mahram (Unmarriageable kin). And Allah The Exalted Knows Best.
What is the ruling on working in the construction project of an Islamic bank`s administration building?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions There is no sin in working for the bank that declares compliance with the rulings of Sharia, in addition to adhering to the rulings of the supervising Sharia committee in the bank itself. This is provided that the committee consists of righteous, trustworthy, specialized scholars. And Allah The Almighty Knows Best.
Is it permissible to repeat the Istikhara (seeking guidance) prayer, and is it a condition that one should sleep after offering it?
All perfect praise be to Allah,The Lord of The Worlds Istikhara is offered once, but it is permissible to repeat it, and sleeping after offering it is not a condition for its validity. And Allah Knows Best.