What is the ruling on wiping over socks?
It is not permissible to wipe over most common socks today because the conditions for wiping are not met. The concession was reported for wiping over leather socks (khuff) and socks (jowrab) with conditions: They must be thick, not allowing poured water to penetrate, enable one to walk in them, be worn while in a state of purity (from ablution), cover the entire foot up to the ankles (meaning covering the protruding ankle bones), and not be torn. And Allah the Almighty knows best.
Is "Bismillāhir-Raḥmānir-Raḥīm" a verse (āyah) of Sūrat al-Fātiḥah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The basmalah ("Bismillāhir-Raḥmānir-Raḥīm") is, without question, a verse (āyah) of the Noble Qur'an, and according to the Shāfi‘ī school, it constitutes a verse of Sūrat al-Fātiḥah itself. Al-Fātiḥah is a pillar of the prayer, and it consists of seven verses, of which the basmalah is one. The prayer is not valid without reciting it, nor if any of the Fātiḥah's verses, letters, or shaddahs (consonant doublings) are omitted or altered.
It is stated in Bushrā al-Karīm (Vol.1/p.202), from the books of the Shāfi‘ī school: "The basmalah is a complete verse of it [i.e., of al-Fātiḥah] in practice — and it suffices, for this to be established, that there be strong probability (ẓann), especially given that this has come very close to certainty (yaqīn), due to the consensus (ijmā‘) of the Companions on its inclusion in the muṣ-ḥaf [the written text of the Qur'an] in its script, despite their extreme diligence in excluding from it anything that did not genuinely belong to it — to the point that they even [carefully regulated] its diacritical dots and vowel markings." And Allah, the Exalted, knows best.
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.
A woman made a wig for herself from her own [previously shed] hair, which she wears on her head after having lost her hair [due to hair loss]. Is this permissible?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Since the hair belongs to the woman herself, the wig can be removed during the obligatory ghusl (ritual bathing), and part of the head can still be wiped during wuḍū' (ablution), there is no sharī‘ah objection to making this wig — provided she does not appear wearing it in front of non-maḥram men (Any males outside a woman's immediate family whom she is permitted to marry under Islamic law), since it is not permissible for them to look at a woman's detached hair.
It is stated in Rawḍat aṭ-Ṭālibīn wa ‘Umdat al-Muftīn: "Whatever it is not permissible to look at while still attached [to the body] — such as the male genitalia, a free woman's forearm, the hair of her head, and a man's pubic hair, and similar matters — it remains unlawful to look at even after it has been detached [from the body], according to the more correct position (al-aṣaḥḥ)." And Allah, the Exalted, knows best.