Does sacrificing one sheep avail for the entire household?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Offering an Udhiyah (sacrificial offering) is a communal Sunnah (Sunnah Kifayah) for members of the same household, provided that their financial maintenance is undertaken by a single provider. By "communal Sunnah," we mean that when one person performs it, the religious recommendation is fulfilled on behalf of the entire household, though the spiritual reward itself belongs uniquely to the one who offered it.
Therefore, if any member of the household performs the sacrifice—even if it is someone who is not legally responsible for the household's expenses, such as the wife or one of the children—the recommendation is fulfilled for everyone in that home. However, the reward does not automatically extend to the other members unless the person offering the sacrifice explicitly intends to share the reward with them—similar to how performing a funeral prayer (Janazah) fulfills the communal obligation for everyone, yet the specific reward is earned by those who actually prayed.
Additionally, a single sacrifice is sufficient for a man who is married to more than one wife. And Allah the Almighty Knows Best.
Does touching women temporarily forbidden in marriage nullify ablution?
It is prohibited to touch, or to shake hands with such women as they are considered strangers, and doing so nullifies ablution.
Is it permissible for a woman to observe voluntary fast without her husband's permission?
A woman is not permitted to observe a voluntary fast (nafl) while her husband is present without his permission.
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.