Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
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.
Who is required to give fidyah for fasting?
Fidyah—feeding one needy person for each missed fasting day—is required for:
1. Those who are permanently unable to fast, such as:
○ Elderly men and women who are too weak to fast.
○ People with chronic illnesses that have no hope of recovery.
2. Pregnant or breastfeeding women who break their fast out of fear for their child (fetus or infant).
3. A person who delays making up Ramadan fasts (qada) until the next Ramadan begins, without a valid excuse.
4. The estate of a deceased person who had missed obligatory fasts and had the ability to make them up but did not do so.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.