What is the meaning of the Prophetic statement that a boy is held in pledge (murtahan) for his 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The first interpretation: That if the boy dies in infancy without an 'aqīqah having been performed on his behalf, he will not intercede for his parents on the Day of Resurrection. This is the position of Imam Aḥmad ibn Ḥanbal, and Imam al-Khaṭṭābī concurred with him, stating: "The finest of what has been said regarding this matter is the position adopted by Aḥmad ibn Ḥanbal." — [Fatḥ al-Bārī by Ibn Ḥajar,{Vol.9/P.594]
The second interpretation: That the child is likened to a pledged object (marhūn) — one from which full benefit and enjoyment cannot be derived until it is redeemed. A blessing is only made complete upon the one blessed when they fulfil the obligation of gratitude (shukr), and the prescribed expression of gratitude for this particular blessing is what the Prophet ﷺ established as Sunnah — namely, the slaughtering of the 'aqīqah on behalf of the newborn as an act of thankfulness to Allah the Almighty and as a supplication for the wellbeing and safety of the child. This is the position of Mullā 'Alī al-Qārī. See: [Mirqāt al-Mafātīḥ Sharḥ Mishkāt al-Maṣābīḥ, Vol.7/P.2688]
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 the ruling on someone who intends to travel to Jeddah for two days — must he enter iḥrām from his place of residence [i.e., before passing the mīqāt]?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Whoever is firmly resolved in his intention to perform ‘Umrah before setting out on his journey, it is unlawful for him to pass beyond his country's mīqāt (the designated boundary point for entering the state of iḥrām) without entering iḥrām. If he does so, he must return to the mīqāt to enter iḥrām from there, provided he has not yet begun performing the rites of the pilgrimage — in which case nothing further is required of him. However, if he does not return, he must offer a sacrifice (sheep/goat), to be distributed among the poor of the Ḥaram.
It is stated in at-Tanbīh fī al-Fiqh ash-Shāfi‘ī (p. 71): "Whoever, intending to perform the rites [of ‘Umrah or Ḥajj], passes beyond the mīqāt and enters iḥrām only after it, must offer a sacrifice. However, if he returns to the mīqāt before beginning any of the rites, the sacrifice is waived from him."
Accordingly: whoever is firmly resolved in his intention to perform ‘Umrah before setting out on his journey must enter iḥrām at the mīqāt of his country through which he passes. Whoever fails to do so, passing beyond the mīqāt without entering iḥrām, and does not return, has sinned, and must repent to Allah, the Exalted; and he must offer a sacrifice, to be distributed among the poor of the Ḥaram. And Allah, the Exalted, knows best.
What is the wisdom behind the legislation of fasting?
Fasting is a divine school from which the believer learns much and trains in virtues that may be needed in life. Among these virtues is patience, as it is the month of patience. Fasting also teaches honesty and consciousness of Allah in both private and public, for there is no observer over the fasting person in abstaining from lawful pleasures except Allah alone.
Fasting strengthens willpower, sharpens determination, and nurtures mercy and compassion among the servants of Allah. It is a struggle against the self, a restraint of desires, a purification of the soul, and a cultivation of goodness.
The Prophetﷺ said: "Allah, the Almighty, said: ‘Every deed of the son of Adam is for him, except for fasting; it is for Me, and I shall reward for it. Fasting is a shield. So when one of you is fasting on a day, let him not engage in obscene speech or raise his voice in anger. If someone insults him or fights him, let him say: I am a fasting person. By Him in whose hand is the soul of Muhammad, the breath of the fasting person is more pleasant to Allah than the fragrance of musk.’" [Bukhari and Muslim]