Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.
What is the stance of Ahlus-Sunnah wal-Jama'ah regarding the historical figure known as 'the Sufyani,' who some say will appear at the end of times? And what is the stance of Ahlus-Sunnah wal-Jama'ah regarding the group that killed Al-Husayn ibn Ali (may Allah be pleased with them), particularly those who directly committed the killing, severed his head, and killed members of his family?
Most of the narrations about the signs of the Hour concerning the Sufyani, who is said to appear before the Mahdi, indicate that he is the leader of the army that will invade the Kaaba, and Allah will cause the earth to swallow them. We disassociate ourselves before Allah from those who killed Al-Husayn Ibn Ali (may Allah be pleased with them), supported his killing, or encouraged it, whether openly or secretly. The inner matters are left to Allah alone. And Allah The Almighty Knows Best.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
What should a woman who delayed making up for missed fast, due to menstruation, till the start of the next Ramadan?
Whosoever broke fasting in Ramadan, and was able to make up for it, but didn`t until the next Ramadan started, is obliged to make up for the missed days, and to pay the ransom as well. However, if he/she wasn`t able to before next Ramadhaan due to an excuse, then he/she should only make up for the missed days. And Allah Knows Best.
