Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?
Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.
Is an elderly or chronically ill person required to pay additional fidyah if they delay it beyond the first year?
An elderly person or someone permanently unable to fast must pay fidyah by feeding one needy person for each missed day.
However, if they delay paying fidyah beyond the first year, no additional fidyah is required.
This differs from someone who delays making up missed Ramadan fasts (qada) without a valid excuse until the next Ramadan begins—such a person is required to pay an additional fidyah for the delay.
What is the wisdom and purpose behind the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Among the wisdoms and purposes of the 'aqīqah are the following:
First: Expressing joy at the blessing of Allah the Almighty, rejoicing in the newborn, and giving thanks to Allah for this gift. Allah the Almighty says (what means): "If you are grateful, I will surely increase you." [Ibrāhīm/7]
Second: Proclaiming and publicising the lineage (nasab) of the child — and the 'aqīqah serves as an appropriate and fitting means to this end.
Third: Gladdening the hearts of family members, relatives, friends, and the poor by gathering them together over a shared meal. And Allah Almighty knows best.
Is it permissible to eat from an Udhiyah slaughtered on behalf of a deceased person?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to eat from the sacrifice (uḍḥiyyah) that is offered on behalf of a deceased person. This is the madhhab (school of thought) of the Hanbalis. In this case, the heirs take the place of the deceased as if he were alive, with the same rights to eat from it, give it in charity, and offer it as a gift.
It is stated in Maṭālib Uli al-Nuhā (Vol.2/P.472): "Offering a sacrifice on behalf of a deceased person is better than offering one on behalf of a living person, because the deceased is unable (to perform deeds) and is in need of reward. It is to be treated like a sacrifice on behalf of a living person in terms of eating, giving charity, and giving gifts." And Allah Almighty knows best.