What should a woman, who has given several births during different months of Ramadhaan, and didn`t make up for them in addition to forgetting the exact number of the days and years in which she had missed fasting, do ?

She should make up the days of Ramadhaan that she missed after estimating their number, and paying the ransom(in food) due on each day that she had delayed. She should also repay the ransom according to the number of years if she was able to fast before that time, but didn`t.

What is the semi-circular structure abutting the Holy Kabah?

It is the Black Stone of the Holy Kabah, and one should pass from behind it while offering Tawaf(circumambulation) because it is part of the Kabah.

Can the Christian widow whose husband is Muslim become an heir of his?

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.