What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.
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.
What is the ruling on swallowing saliva while fasting?
It is permissible for a fasting person to swallow their saliva because avoiding it would cause undue hardship and excessive strictness in religion. Islam discourages such excessiveness since Allah the Almighty intends ease for His followers and does not intend to put them in hardship.
Is it Sunnah to cook the meat of the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah not to distribute the meat of the 'aqīqah raw. Rather, it is recommended to cook it with something sweet — such as raisins or honey — as a good omen and expression of hope for the sweetness of the newborn's character and conduct throughout their life. And Allah Almighty knows best.