A woman used contraceptive pills, and her menses exceeded (15) days, is it permissible for her to fast?
The maximum of menstrual blood is (15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah (bleeding outside the monthly period), and in this case she should perform Ghusl (ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses. And Allah Knows Best.
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.
Is it permissible for a wife`s family to demand her husband to divorce her although she doesn`t want that?
It is forbidden for them to do that in case their daughter doesn`t want divorce unless there was a sin that continues as long as the marriage survives.
Is it permissible for a man to lie to his wife? Is it permissible for a man to abandon his wife to work in Saudi Arabia, without her approval, although he is wealthy?
All perfect praise be to Allah, the Lord of the Worlds; may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
The Messenger of Allah commanded men to treat women kindly, so marital problems should be solved through understanding, and whatever causes harm to a woman is forbidden. And Allah The Almighty Knows Best.