What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.
Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.
When is a child instructed to fast?
A child is instructed to fast at the age of seven if they are capable of fasting and have reached the age of discernment, by analogy to prayer. They should be encouraged but not forced, so they can become accustomed to it. It is obligatory for their guardian, whether a father or another, to instruct them.
Which is superior: The Udhiyah (Sacrificial Offering) or giving its value in Charity (Sadaqah)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Performing the Udhiyah (sacrificial offering) is superior to giving its monetary value as charity (Sadaqah) to the poor and needy. This is because the Udhiyah is one of the manifest symbols of the religion. Allah the Almighty says {what means}: "That [is so]. And whoever honors the symbols of Allah - indeed, it is from the piety of hearts." [Al-Hajj/32]. This is further supported by the explicit and authentic Hadiths regarding its virtue, and the fact that the Prophet ﷺ and the Rightly Guided Caliphs after him consistently performed the sacrifice. And Allah the Exalted knows best.