Is it incumbent on a family to provide for its old handicapped son and take care of him?
The family and relatives - e.g. brothers - of such a person are obliged to spend on him and take care of him if he didn`t have money of his own.
Should a pregnant woman who broke fast because of pregnancy make it up, and is a ransom due on her?
The pregnant and the suckling, if they fear for their health, may break their fast and make up for it, and no ransom is due on them. However, if they broke fast in fear for the fetus and the baby, then they are obliged to make up for it, and pay the ransom which is feeding a needy person for each of the missed fasting days. And Allah Knows Best.
My father placed shares worth twenty dinars in one of the banks, and their value doubled to become five thousand dinars. When my father passed away, one of the scholars told us that it is permissible for us to take the money. What is the ruling on this money, considering that it comes from a bank and involves interest (Riba)?
Allah The Almighty Said (What means): "And if you repent, then for you is the principal of your wealth. You do not wrong, nor are you wronged." [Al-Baqarah/279]. This is the precautionary ruling regarding what you are asking about. You are entitled to the principal amount, and you should give the excess as charity to the poor and needy. If you are poor, you may take from it. And Allah The Almighty Knows Best.
Should Al-Basmalah (i.e. saying Bismillaaahi Ar-Rahmaani Ar-Raheemi) be recited after Takbeerat Al-Ihram (saying Allahuakbar) which marks the beginning of prayer?
All perfect praise be to Allah,The Lord of The Worlds A praying person is obliged to recite Al-Basmalah at the beginning of Chapter Al-Faatihah, and in every Rak`ah (unit of prayer) because it is a verse of it. And Allah Knows Best.