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 the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
What is recommended for a Muslim to say on Laylat al-Qadr?
On Laylat al-Qadr, it is recommended for a Muslim to recite the supplication (du‘a) that the Prophet ﷺ taught Aisha (may Allah be pleased with her):
"O Allah, You are Most Forgiving, and You love forgiveness, so forgive me." [Narrated by Al-Tirmidhi]
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.