What is the Islamic ruling on the aqiqa?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is a confirmed Sunnah (sunnah mu'akkadah). Two sheep are to be slaughtered for a newborn boy, and one sheep for a newborn girl. This is established by numerous Prophetic traditions, among them:
The narration of Samurah ibn Jundub, may Allah be pleased with him, who reported that the Messenger of Allah ﷺ said: "Every child is held in pledge for his 'aqīqah, which is slaughtered on his behalf on the seventh day, and he is named, and his head is shaved." — Narrated by al-Tirmidhī, who graded it as ḥasan ṣaḥīḥ.
And the narration of 'Ā'ishah, may Allah be pleased with her, who said: "The Messenger of Allah ﷺ commanded us to slaughter one sheep as 'aqīqah for a girl, and two sheep for a boy." — Narrated by Aḥmad and Ibn Mājah.
The imperative in these narrations is understood to denote recommendation rather than obligation, based on the ḥadīth of 'Amr ibn Shu'ayb, on the authority of his father, on the authority of his grandfather, who said: The Messenger of Allah ﷺ was asked about the 'aqīqah, whereupon he said: "Allah does not love 'uqūq" — as though he disliked the name itself — and then said: "Whoever has a child born to him and wishes to offer a sacrifice on their behalf, let them do so: two equivalent sheep for a boy, and one sheep for a girl." — Narrated by Aḥmad and Abū Dāwūd.
The legal inference drawn from this narration is that the Prophet ﷺ linked the slaughter to the wish and willingness of the individual, saying: "whoever wishes to offer a sacrifice... let them do so" — thereby indicating that the 'aqīqah is recommended (mustaḥabb) and not obligatory (wājib).
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.
Do pregnant and breastfeeding women have to fast?
Pregnant and breastfeeding women are required to fast. However, if fasting causes them harm or unusual hardship, they may break their fast but must make up for the missed days later.
If they break their fast solely out of fear for the fetus or the child, then they must both make up the fast and give fidyah (feeding a needy person for each missed day), as the benefit of breaking the fast was only for the child.
What is the ruling on the ablution of one from whom blood exits from his nose or a wound?
Blood flowing from a wound or a nosebleed does not invalidate ablution. However, performing ablution is recommended to avoid scholarly disagreement with those who make ablution obligatory after blood flows. And Allah the Almighty knows best.