What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. 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.
Who is obligated to fast?
The one obligated to fast is the Muslim who is of sound mind, mature, capable of fasting, and free from obstacles such as menstruation or postpartum bleeding. And Allah Knows Best.
I`m a Muslim woman and have fallen in love with a Christian man. Supposing that he embraced Islam. Is it permissible that he proposes to me?
Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The relationship between you two is forbidden; however, if he wants to embrace Islam then he should pay a visit to a Sharia court. Once he becomes a Muslim, we will address the matter of proposing to you. And Allah The Almighty Knows Best.