Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.
Is it permissible for household members to pool money for the Udhiyah and gift it to one of them?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for members of a household to pool their money together and gift the total amount to one individual among them so that he may offer the sacrifice (Udhiyah). In this case, the family members receive the reward for giving charity (Sadaqah), and the one performing the sacrifice includes them in the spiritual reward (Thawab).
Furthermore, slaughtering a single sheep (on one's own) is considered religously better than participating as one of seven people in the sacrifice of a cow or a camel. And Allah the Almighty 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.
What is the ruling on preparing food for someone who is not fasting in Ramadan?
It is forbidden to prepare food for someone who is breaking their fast without a valid excuse in Ramadan.
Doing so would be assisting in sin, and assisting in sin is itself a sin.
Allah says {what means}: "but help ye not one another in sin and rancour" [Al-Mai`dah/2]