What should a praying person who doubts having offered one, or two prostrations in the third Rakah (unit of prayer) do?
Whoever has doubts about their prayer should consider what is less i.e. the above person should offer another Sajda (prostration) and complete his/her prayer, then offer Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.
Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
Is it permissible for a person to sever ties with his sister because her husband had quit prayer and done him harm?
A sister is a blood-relative and maintaining blood-relations is obligatory in Islam. As regards her husband, he should be invited to the way of Allah with wisdom and beautiful preaching.
