Is it valid to perform the obligatory prayer while sitting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Standing (Al-Qiyam) while having the ability to do so is one of the pillars (Arkan) of the prayer; the obligatory (Faridah) prayer is not valid without it. However, whoever is unable to stand may pray sitting down. As for voluntary (Nafilah) prayers, it is permissible to pray them sitting even if one is able to stand, but the one sitting receives half the reward of the one who prays standing. And Allah the Exalted knows best.
What is the ruling on applying perfume while fasting?
Applying perfume does not break the fast. However, it is better to avoid it, as fasting is a practice of simplicity and restraint, while perfume is a form of luxury.
What is the ruling on performing ablution (wudu') and ritual bathing (ghusl) with Zamzam water?
It is permissible to perform ablution and ritual bathing with Zamzam water. However, scholars disliked using it for cleaning after relieving oneself (istinja'). And Allah the Almighty knows best.
Is it permissible to include others in the reward of one`s sacrifice?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible for the one offering a sacrifice (al-muḍaḥḥī) to include another person in the reward of the sacrifice, but it is not permissible for them to share in the price of the sacrifice. It is stated in Mughnī al-Muḥtāj (Vol.6/P.137) by al-Khaṭīb al-Shirbīnī: "If he includes another in the reward of his sacrifice and slaughters it on his own behalf, it is permissible." And Allah Almighty knows best.