Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.
Is it acceptable to perform the Aqiqah for a male child by slaughtering and distributing the first sheep, and bringing the second one cooked from the restaurant?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to slaughter the first sheep with the intention of Aqiqah (the newborn's sacrificial offering) and distribute it entirely [uncooked], and to slaughter the second sheep and have it cooked at a restaurant to bring home for the household. However, it must be noted that it is obligatory to give some portion of the Aqiqah in charity to the poor, even if it is a small amount, though it is preferable to send the food cooked to them.
Buying a pre-cooked, ready-made sheep from a restaurant does not suffice as an Aqiqah. However, if an agreement is made with the restaurant to explicitly slaughter a sheep with the intention of Aqiqah for the newborn, and then cook it afterward, this is permissible.
In conclusion, slaughtering the sheep and distributing it with the intention of Aqiqah is permissible, and through it, the foundational prophetic tradition (Sunnah) is fulfilled. As for simply buying a cooked sheep from a restaurant that was not specifically slaughtered with the intention of Aqiqah, it will not count as such. Conversely, if the restaurant owner is commissioned (Wakala) to handle both the slaughtering and the cooking as an Aqiqah, it is valid—provided that a portion of it, even if small, is given in charity, which is estimated to be approximately half a kilogram of meat. And Allah the Almighty knows best.
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 praying behind a disliked Imam?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is mildly disliked (Makruh Tanzihan) for a man—other than the permanent designated Imam (Imam Ratib)—to lead people in prayer if the majority of them dislike him due to a religiously blameworthy reason (Amr Madhmum Shar‘an), such as associating with open sinners (Fussaq), for example. As for the followers who dislike him, the prayer behind him is not disliked for them. However, if less than the majority dislike him, or if the majority dislike him for a reason that is not religiously blameworthy, then his leading the prayer is not disliked. And Allah the Exalted knows best.