Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?
It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.
What is the ruling on the Friday bath (ghusl al-Jumu'ah)?
The Friday bath is a confirmed Sunnah, based on the Prophet's (peace be upon him) saying: "Whoever performs ablution on Friday, it is good for him, and whoever takes a bath, bathing is better." (Reported by Abu Dawud and al-Tirmidhi who said it is a hasan hadith). It is recommended for everyone who wants to attend the Friday prayer, even if they are not from its usual attendees, like a woman or a boy.
If a person is in a state of major impurity (junub) and intends by his bath both lifting the major impurity and the Friday bath, he achieves both. If he intends only one of them, he achieves only what he intended. And Allah the Almighty knows best.
There are olive trees within the precincts of the mosque, and my father covers the costs of electricity, water, and other needs of the mosque. Is it permissible for him to take the olive harvest?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
If trees and fruit-bearing crops are planted in a mosque for the mosque itself, they may only be spent on the mosque’s interests. If they were planted for the public way (musabbalah), that is, for the general public, then any Muslim who enters the mosque may eat from them. If the planter’s intention is unknown, they are treated like those dedicated for public use, wherever custom has so run.
It is stated in Tuḥfat al-Muḥtāj (Vol.6/p.295): “The fruit of a tree planted for the mosque within it is not freely permitted without compensation. Rather, the imam spends its equivalent value on the mosque’s interests. The tree left its planter’s ownership here without any verbal declaration because of the evident indication. The case of planting it for the mosque excludes planting it as musabbalah, in which case eating from it without compensation is permissible, and likewise if his intention is unknown, where custom has so run. The tree may be uprooted from the mosque if the imam sees fit. Indeed, if he makes the plot a mosque while a tree stands in it, the imam may uproot it, even if the endower included it within the endowment (waqf).”
The father is a donor (mutabarriʿ), so he is not entitled to take anything in return for his donation to the mosque.
The Ministry of Awqāf is the body that supervises the affairs of endowments, so it must be consulted and the Sharīʿah and administrative instructions regulating such matters must be considered. And Allah Almighty knows best.