Who is the one required to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered by the guardian of the newborn — the one upon whom the child's financial maintenance is obligatory — provided he is financially capable of doing so. 'Alī ibn Abī Ṭālib, may Allah be pleased with him, reported: "The Messenger of Allah ﷺ performed the 'aqīqah for al-Ḥasan with one sheep." — Narrated by al-Tirmidhī. And Allah 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.
Is it permissible to include others in the reward of one`s sacrifice?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for the person offering an Udhiyah (sacrificial offering) to include others in the spiritual reward of the sacrifice. However, it is not permissible for multiple people to jointly share the purchase price of a single sheep or goat, unless one person gifts the money to the other.
It is stated in Mughni al-Muhtaj (6/137) by Al-Khatib al-Shirbini:
"If a person includes someone else in the reward of his sacrifice and slaughters it on his own behalf, it is permissible."
It should be carefully noted that including someone else in the reward of one's sacrifice is completely distinct from offering a sacrifice on behalf of someone else. And Allah the Almighty Knows Best.
What is the ruling on brown discharge before the menstrual period? Is it considered part of menstruation (Hayd)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Dusky discharge (Kudrah), reddish discharge (Humrah), and yellowish discharge (Sufrah) are all considered menstruation (Hayd) if they occur during the time of the menstrual cycle. If their duration exceeds a day and a night, and the period persists from the first sight of the discharge until the cessation of the menstrual blood—provided the total duration does not exceed fifteen days—then all of it is menstruation. However, if the duration exceeds fifteen days, then the discharge is not considered menstruation, but rather chronic irregular bleeding (Istihadah). And Allah the Exalted knows best.