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.
Is it permissible to authorize charitable organizations to perform the Udhiyah on one`s behalf?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to authorize charitable organizations to perform the sacrifice (Udhiyah) on one’s behalf. However, if these organizations undertake the slaughtering for a group of people, those in charge of the slaughtering must maintain lists of the names of those who authorized them. Furthermore, at the time of slaughter, the slaughterer must intend that the specific sacrifice is on behalf of a specific person. And Allah the Almighty knows best.
What is required of a traveler or a sick person if they broke their fast and then their excuse ceased?
If a traveler settles or a sick person recovers after having broken their fast, it is recommended for them to refrain from eating and drinking for the rest of the day, but it is not obligatory.
Does post-natal bleeding (Nifas) stop before forty days after childbirth?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Yes, post-natal bleeding (Nifas) can cease before the completion of forty days. If the bleeding stops completely and its return is not expected, the woman has attained ritual purity (Taharah), even if forty days have not yet passed. And Allah the Exalted knows best.