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 for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.
An engineer has to work in a circuit system of a non-Islamic bank. What is the ruling on the income she receives from doing this job?
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.
Necessity lies in fearing for one`s life, honor or mind, so the wage received for doing a forbidden job is equally forbidden. Kindly contact the Iftaa` Department to further clarify the nature of your work. And Allah The Almighty Knows Best.
What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. And Allah Knows Best.