Is Zakah (obligatory charity) due on the items used in the trading process such as: cars , shops etc..?
No Zakah is due on equipments used in the trading process such as cars and the like.
Does nosebleed during the day in Ramadan affect the validity of fasting?
A nosebleed does not affect the validity of fasting unless some of the blood reaches the body cavity or the person intentionally swallows it. In such a case, their fast is invalid, and they must refrain from eating and drinking for the rest of the day and make up for that day later.
Is it permissible to divide a single Sa‘ of Zakat al-Fitr—or its equivalent value in cash—among more than one poor person?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Zakat al-Fitr is estimated at one Sa‘ per person, but the number of people to whom this Sa‘ can be given has not been specified. For this reason, it is permissible to distribute a single Sa‘ among more than one poor person. And Allah the Exalted knows best.
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.