Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.
What is the ruling on a woman who takes medication to delay menstruation for fasting?
If a woman takes medication (to delay menstrual period) and does not experience menstruation, her fast is valid. However, she is not advised to do so unless there is a necessity.
If the medication harms her, even potentially, it is forbidden (haram) for her to take it.
What is the ruling of Islamic Law on Making up Prayers Missed before Reaching Puberty?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Among the conditions for accountability for one's actions in the Hereafter is taklīf (religious legal responsibility) — meaning, possessing sound reason and having reached puberty. The signs of puberty are: nocturnal emission, menstruation, or reaching the age of fifteen [lunar years].
Whoever missed prayers before reaching puberty is not obligated to make them up, since taklīf did not yet apply to him at that time. Our master, the Prophet ﷺ, said: "The pen has been lifted from three: from the child until he reaches puberty, from the sleeping person until he wakes, and from the insane person until he regains sanity." [Related by Abū Dāwūd]
The method for making up missed prayers and fasts has already been explained in Fatwa No.
2705, and Fatwa No.
876. And Allah, the Exalted, knows best.