Who is the one required 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 by the guardian of the newborn — the one upon whom the child's financial maintenance is obligatory — provided he is financially capable of doing so. 'Alī ibn Abī Ṭālib, may Allah be pleased with him, reported: "The Messenger of Allah ﷺ performed the 'aqīqah for al-Ḥasan with one sheep." — Narrated by al-Tirmidhī. And Allah Almighty knows best.
Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?
Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.
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.
The Prophet ﷺ said: "There will emerge from my nation people who will drink the Qurʾān as they drink milk" — is this ḥadīth authentic, and what does it mean?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
ʿUqbah ibn ʿĀmir, may Allah be pleased with him, narrated that the Messenger of Allah ﷺ said: "There will emerge from my nation people who will drink the Qurʾān as they drink milk." (Reported by al-Ṭabarānī in al-Muʿjam al-Kabīr, and cited by al-Haythamī in Majmaʿ al-Zawāʾid, who stated: "Its narrators are trustworthy.")
The meaning of this ḥadīth is that there will emerge from this blessed nation people who recite the Holy Qurʾān without reflecting upon its meanings or pondering its rulings — the noble verses passing over their tongues just as milk passes over them when it is drunk, leaving no trace of thought, understanding, or contemplation behind. [See: al-Taysīr bi-Sharḥ al-Jāmiʿ al-Ṣaghīr,Vol.2/P.63] And Allah the Almighty knows best.