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.
What is the ruling of Islamic Law on obtaining financing from Islamic banks by bringing invoices in prior arrangement with the seller, then taking the cash after the financing is approved — with the purpose of settling debts and buying a car?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It appears from the transaction described that its underlying purpose is to obtain cash through resorting to a legal artifice (ḥīlah/tawarruq-style trick), and it is not permissible to engage in such trickery or to coordinate with the various parties merely to obtain liquidity. This is because such artifices bring the sale closer in reality to a ribā-based (usurious) transaction, even if it outwardly appears otherwise.
The Prophet ﷺ said: "Do not commit what the Jews committed, thereby making lawful what Allah has made unlawful through the flimsiest of tricks." This was related by Ibn Baṭṭah in his book Ibṭāl al-Ḥiyal (p. 47), and many scholars have graded it as ḥasan (sound/acceptable).
We have already explained the impermissibility of engaging in such deceptive dealings with Islamic banks in Fatwa No. 516, so please refer to it. And Allah, the Exalted, knows best.
Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (Makruh) for a person in a state of minor ritual impurity (Hadath Asghar) to perform the Adhan. However, if he does so, his Adhan is considered valid and fulfills the sunnah of the Adhan despite it being disliked. And Allah the Exalted knows best.
What is the ruling on sacrificing a castrated animal or one with a missing tail?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to sacrifice a castrated sheep; as it has been established that the Prophet (peace be upon him) sacrificed:
"...two large, fat, horned, white-and-black, castrated rams (Mawju'ayn—meaning having crushed testicles)." [Narrated by Ibn Majah in his Sunan].
It is not permissible to sacrifice an animal that is missing its tail, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, or udder; such an animal is valid for sacrifice. And Allah the Almighty knows best.