When is it Sunnah to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered on the seventh day from the birth of the newborn. According to the sounder position, the day of birth itself is counted as the first of the seven days. Thus, for example, if the child is born on a Saturday, the 'aqīqah is to be slaughtered on the following Friday. If the child is born at night, the count begins from the day that follows. And Allah Almighty knows best.
Is fasting obligatory for a child?
Fasting is not obligatory for a child until they reach puberty. Puberty is determined by well-known signs, the most common of which are: nocturnal emission (for both males and females), menstruation (for females), or reaching the age of fifteen lunar years.
A guardian must instruct their children to fast once they reach the age of discernment, which is around seven years old, if they are capable of fasting.
What is required of one who doubts the number of rakʿāt during prayer?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If a person doubts the number of rakʿāt he has prayed, he should build upon the lesser number, as that is what he is certain of. He should then perform the prostration of forgetfulness (sujūd al-sahw) before the final salām at the end of the prayer. ʿAṭāʾ ibn Yasār narrated that the Messenger of Allah ﷺ said: "When any one of you is in doubt during his prayer and does not know whether he has prayed three rakʿāt or four, let him pray one more rakʿah and then perform two prostrations while seated before the salām. If the rakʿah he prayed was a fifth, these two prostrations will make it even; and if it was the fourth, then the two prostrations serve as a humiliation for the devil." (Reported by Abū Dāwūd.)
It is stated in al-Muqaddimah al-Ḥaḍramiyyah — one of the foundational texts of the Shāfiʿī school: "If one doubts whether he has prayed three rakʿāt or four, he is obliged to build upon the lesser number."
However, if such doubt recurs repeatedly and reaches the level of obsessive whispering (waswasah), he should not build upon the lesser number in that case — rather, he should build upon the greater number. And Allah the Almighty knows best.
Who should pay the Zakah (obligatory charity) from the orphan`s money?
His/her guardian, and if the latter fails to do so, then the orphan himself/herself is obliged to pay the Zakah once he/she reaches puberty, and is capable of handling his/her own affairs. And Allah Knows Best.