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.
Is it Sunnah to cook the meat of the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah not to distribute the meat of the 'aqīqah raw. Rather, it is recommended to cook it with something sweet — such as raisins or honey — as a good omen and expression of hope for the sweetness of the newborn's character and conduct throughout their life. And Allah Almighty knows best.
What is the ruling on a woman who learns of her divorce or her husband's death after her *ʿiddah* has ended? And does the *ʿiddah* of a woman who abandoned mourning (*iḥdād*) for the whole period of the *ʿiddah*, or part of it, still end, even though she knew that abandoning it is forbidden?**
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The waiting period of a widow who is not pregnant is four months and ten days, based on the saying of Allah Almighty (which means): “And those of you who die and leave wives behind, they shall wait concerning themselves for four months and ten days” [al-Baqarah/234]. If she is pregnant, her ʿiddah ends with the delivery of her child. The ʿiddah is calculated by lunar months and begins from the date of death.
If her ʿiddah ends before she learns of her husband’s death, or of his divorcing her, she does not observe the ʿiddah upon learning of it, because her ʿiddah has already ended.
It is stated in al-Bayān fī Madhhab al-Imām al-Shāfiʿī (Vol.11/p.41), one of the books of the Shāfiʿī school: “If a man divorces his wife, or dies while he is absent from her, her ʿiddah is from the time of the divorce or from the time of death. If she does not know of the divorce or the death until her ʿiddah period has ended, then her ʿiddah has ended. If she learns of it before the end of the ʿiddah period, she completes her ʿiddah counting from the time of the divorce or death.”
As for a woman who abandoned mourning throughout the ʿiddah while knowing that it is forbidden, she is sinful, although her ʿiddah has nonetheless ended. And Allah Almighty knows best.
Does excessive sleep during Ramadan invalidate fasting?
Sleeping a lot in Ramadan does not invalidate the fast, but a Muslim may miss out on great rewards from prayer, Quran recitation, and acts of worship due to excessive sleep.