Is it permissible for me to name my daughter "Leen"?
“Leen” means “ease”, and there is no harm in giving your daughter that name.
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 missed days of Ramadan after estimating their number, and paying the ransom (in food) due on each missed day that she had delayed making up. In addition, she is obliged to repay the ransom according to the number of years if she was able to fast before that time, but didn`t.
Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?
Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.
A man break his fast once during Ramadan and he already have an expiation of fasting for two consecutive months. He fasted for a month and passed away. Is it permissible for his sons to fast the remaining month equally?
Fasting for expiation must be performed consecutively. I advise his children to feed sixty poor people, giving each one half a kilogram of rice or its monetary equivalent. This is because if a living person is unable to fast, they are required to feed sixty poor people, and death constitutes an inability. And Allah The Almighty Knows Best.