Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
What is the ruling on the ablution of one from whom blood exits from his nose or a wound?
Blood flowing from a wound or a nosebleed does not invalidate ablution. However, performing ablution is recommended to avoid scholarly disagreement with those who make ablution obligatory after blood flows. And Allah the Almighty knows best.
Is it permissible for women to gather in one of their homes to pray Tarawih?
Yes, it is recommended (mustahabb) for women to pray Tarawih in congregation if they gather, even if it is not in the mosque.
In fact, praying at home is better for them, as it avoids the potential concerns associated with going to the mosque.
What is the ruling on a woman using contraception without her husband's knowledge if he is mistreating her?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is not permissible for a woman to use any means of delaying pregnancy without her husband's knowledge, consent, and mutual agreement. This is because having children is a sharʿī right belonging to both spouses equally in Islamic law. Imām al-Māwardī, may Allah have mercy upon him, stated: "The right to a child from a free woman is shared between them both" — meaning between the two spouses. [al-Ḥāwī al-Kabīr, 9/320]
It is therefore not permissible for either spouse to make a unilateral decision regarding the prevention of pregnancy without the consent of the other. We advise both spouses to discuss the matter with wisdom and mutual respect, so as to resolve any disagreement and arrive at a suitable solution that serves the interests of them both. And Allah the Almighty knows best.