What is the ruling on istinja' after urination, and is it done with water and soap or with water only?
Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.
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.
What is the ruling of Islamic Law on applying perfume before entering the state of ihram
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Applying some perfume (ṭīb) before entering the state of iḥrām does not affect the validity of the Ihram, even if its trace remains after the iḥrām has begun. Indeed, it is sunnah for the pilgrim performing Ḥajj or ʿUmrah to perfume himself before iḥrām.
The scholar Nawawī al-Jāwī (may Allah have mercy on him) said: “The third of them is applying perfume to the body shortly before it, that is, before iḥrām, whether the one entering iḥrām is male or otherwise, young or old, married or unmarried. The recommendation applies after performing the ritual bath (ghusl), and it is fulfilled with any perfume whatsoever, though the best is musk, mixed with rose water or the like. There is no objection to the perfume remaining on the body after iḥrām; however, if a woman becomes bound by the mourning observance (iḥdād) after entering iḥrām, she must remove it. As for perfuming the garment, it is merely permissible, not recommended, according to the reliable position (al-muʿtamad). But if one removes his perfumed garment while the scent is still present in it and then wears it again, he is liable for the fidyah (expiation).” [Nihāyat al-Zayn, Vol.1/212]. And Allah Almighty knows best.
What is the ruling of Islamic Law on one who died owing debts and left no wealth? Is it obligatory upon the heirs to settle these debts?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The general rule is that if a person dies owing rights to other people, such as debts, these are settled from his estate, if he left any wealth, before the estate is divided. The Prophet (peace and blessings be upon him) said: “The believer's soul is suspended by his debt until it is settled for him.” Graded ḥasan by al-Tirmidhī. Repayment of debts takes precedence over the heirs’ right to inheritance.
If the deceased left no estate, or left wealth that was insufficient to cover his debts, it is not obligatory for the heirs to pay from their own wealth, but it is recommended for them to do so, because the deceased’s dhimmah (legal liability) remains occupied by the debt. It is reported in some narrations that he remains held in suspension until his debt is paid, and it is not part of filial righteousness for a child to leave his father’s dhimmah burdened with debt.
All of the children may contribute to settling the debt on behalf of their father and cooperate in doing so, even in installments, according to their ability. And Allah Almighty knows best.