Is it permissible for a menopausal woman who has blood discharges to fast?
If she reached the age of menopause, and her menses stopped, but later she saw blood discharges that lasted a complete day and night (24) hours, then it is menstrual blood. Still, if these blood discharges lasted less than a complete day and night (24) hours, then it is not menstrual blood, but it is bleeding outside the monthly period (Istihadah), and it does not prevent her from prayer and fast, but she has to make ablution for every prayer.
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.
I wish to Pray at the Mosque, but I couldn't because I am a Woman. How can I get such a Reward?
All perfect praise be to Allah The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions Abdullah Ibn Masood (May Allah be Pleased with him) reported that the Prophet (PBUH) said: "Her prayer inside her home is better than its courtyard, and her prayer in her own bedroom is better than inside her home." [Abu Dawood]. Her staying at home, and not going to the mosque in obedience to Allah`s injunctions entails a great reward similar to that bestowed on a man for going to the mosque since the Mercy and Blessings of Allah Prevails. And Allah Knows Best.
Is it permissible for a man to marry up to four wives (polygamy in Islam) for pleasure although he can`t afford that?
It is desirable for the man to have one wife if there was no need for him to have more, if he can't afford marriage forthcoming expenses.