Does the intention (niyyah) of the principal (muwakkil) suffice for the sacrifice (dhabḥ) of the udhiyyah?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person appoints an agent (wakīl) to perform the slaughter (dhabḥ) on their behalf, the intention (niyyah) of the principal (the one appointing the agent) suffices, and there is no need for the agent to have this intention himself. In fact, even if the agent is unaware that he is performing the sacrifice on someone's behalf as an udhiyyah (sacrificial offering), this does not affect its validity. And Allah, the Most High, knows best.
Is vomit among the nullifiers of Wudu (ablution)?
Vomit does not nullify Wudu, but it is a Najaasah (impurity) that requires rinsing the mouth and washing whatever became dirty by it since the prayer becomes valid only after the removal of Najaasah. And Allah Knows Best.
How many Rak`ahs (unit of prayer) are offered in Witr prayer?
All perfect praise be to Allah, The Lord of The Worlds Witr (an odd number prayer performed between Isha`a and Fajr) is offered with a minimum of one Rak`ah, and a maximum of eleven, but offering three Rak`ahs is the minimum of its complete form. And Allah Knows Best.
If the menses lasted for over than 9 to 10 days, considered menstruation?
If the duration of the bleeding does not exceed fifteen days, it is all considered menstruation, even if the usual pattern changes.