Am I permitted to perform more than one prayer within single ablution?
You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified.
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.
Is the `Iddah (waiting period) of the divorced effective from the time the divorce took place, or from the time of registering it at the court?
It is considered effective from the time the divorce took place, and not from the time of registering it at the court.
Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram(Marriageable) to her.