What is the ruling on the prayer of one who said "Subḥāna Rabbiya al-ʿAẓīm" in prostration (*sujūd*) and forgot to correct it?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Saying “Subḥāna Rabbiya al-ʿAẓīm” in bowing (rukūʿ) and “Subḥāna Rabbiya al-Aʿlā” in prostration (sujūd) is one of the hayʾāt (non-essential sunnahs) of the prayer. Whoever omits it, whether deliberately or by forgetfulness, or replaces it with another remembrance (dhikr), his prayer is valid and he does not perform sujūd al-sahw. Shaykh al-Islām Imam al-Nawawī (may Allah have mercy on him) said: “Our school holds that one does not prostrate for omitting the audible or silent recitation, the tasbīḥ, and the rest of the hayʾāt.” [al-Majmūʿ, Vol.4/p.127]
If he performs sujūd al-sahw for something that does not call for it, his prayer is invalidated, because he introduced a prostration of forgetfulness without a cause, and he must repeat the prayer. The exception is one who did so out of forgetfulness or ignorance, whether because he recently entered Islam or because he lives far from scholars; he is excused and his prayer is not invalidated.
It is stated in Mughni al-Muḥtāj (Vol.1/p.417): “It is stated in al-Anwār: If he does something that does not call for sujūd al-sahw, thinking that it does, and then prostrates, his prayer is not invalidated if he is ignorant because he recently entered Islam or because he is far from scholars.”
Since this issue is hidden from the laity, as it is among the subtleties of knowledge, and the laity are excused for ignorance of whatever is of such a nature, and their act of obedience is not invalidated because of it, it may be said that the prayer of one who has not acquired knowledge of the issue is not invalidated. As for after knowing it, the prayer is invalidated.
Whoever realizes while still in the prayer that his prostration was out of place, it is sunnah for him to perform sujūd al-sahw. And Allah Almighty knows best.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.
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 sending blessings and peace upon the prophet (PBUH) after the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is a Sunnah to send blessings and peace (As-Salat wa al-Salam) upon the Prophet ﷺ after the Adhan and the Iqamah, for both the caller (Mu’adhin) and the listener. It is permissible to do so aloud after the conclusion of the Adhan. However, it is preferable to maintain a brief pause between the words of the Adhan and the prayers upon the Prophet ﷺ, so that people do not mistakenly assume that sending blessings upon him is an integral part of the Adhan itself. And Allah the Exalted knows best.