What is the ruling on performing istinja' before every ablution?
Istinja' is not from the conditions for the validity of ablution. It is only obligatory for prayer when there is impurity from urine or stool on the private part, or if there is fear of the impurity spreading to the body or clothing. And Allah the Almighty knows best.
Is it permissible for a woman to give the ransom (Fidyah) for breaking her fast to her granddaughter (her son`s daughter)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for a woman to give the ransom (Fidya) for breaking her fast in Ramadan to her granddaughter (her son’s daughter), provided that the girl is poor and her basic needs are not being met by the maintenance (Nafaqah) of those who are lislamically obligated to provide for her. And Allah the Exalted knows best.
What is the Islamic ruling on eating from the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is recommended (mandūb) to eat from the 'aqīqah, unless it was vowed (mandhūrah). If the 'aqīqah was made as a vow, then it is prohibited to eat from it, and it becomes obligatory to distribute the entirety of it in charity to the poor. And Allah Almighty knows best.
Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. And Allah Knows Best.