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.
What is the ruling on praying seated due to severe obesity, given that I experience hardship in performing the prayer — especially when rising from the ground after sujūd to perform the next rak‘ah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Standing, when one is able to do so, is a pillar of the prayer. However, whoever would experience severe, intolerable hardship, or fears harm to himself or to a limb due to obesity, or finds that standing causes him to lose his khushū‘ (humble focus and concentration) in prayer, then there is no objection to his praying seated on a chair or on the ground, performing rukū‘ (bowing) and sujūd (prostration) through gesture — provided that the gesture for sujūd is made lower than that for rukū‘. Whoever is able, at any point, to properly perform any one of these pillars, is obligated to perform it in full; for omitting it is a concession that applies only in cases of genuine inability. The Prophet ﷺ said: "When I command you to do something, do of it whatever you are able." (Related by al-Bukhārī). As the scholars of fiqh have established: what remains possible is not waived on account of what is difficult.
The criterion for determining genuine inability, as chosen by Imam al-Ḥaramayn al-Juwaynī (raḥimahullāh), is that the worshipper experiences hardship that causes him to lose his khushū‘.
As for voluntary (nafl) prayer, there is no objection to performing it while seated, even if one is able to stand. However, rukū‘ and sujūd must still be performed [in their proper physical form] by anyone who is able to do so. And Allah, the Exalted, 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.
What is the ruling on forgetting an integral of the prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Whoever forgets an integral (Rukn) of the prayer and remembers it before reaching the equivalent point in the subsequent unit (Rak'ah), must return to it (i.e., perform it) and complete his prayer, then perform the prostration of forgetfulness (Sujud al-Sahw) at the end of his prayer. However, if he remembers it after reaching the equivalent point in the subsequent unit, the Rak'ah in which the integral was forgotten is invalidated, and the current unit takes its place; he then completes a full Rak'ah to compensate and performs the prostration of forgetfulness.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.1/P.543): 'If he becomes certain at the end of his prayer, or after the Salam—provided the interval is not long according to custom and he has not stepped on an impurity—that he omitted a prostration from the final Rak'ah, he must perform it and repeat the Tashahhud, as his previous Tashahhud occurred before its proper place. If the omission was from a Rak'ah other than the final one, he must perform a full Rak'ah, because the deficient unit was completed by a prostration from the subsequent one, rendering the rest of that subsequent unit void.' And Allah the Exalted knows best.