Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.
What is the ruling on the fasting of a woman who has reached menopause if menstrual blood flows?
If a woman reaches the age of menopause (which is usually sixty-two) and her menses have ceased, then she sees blood after that, and its duration is not less than a day and a night (24 hours), it is menstruation (hayd). If it is less than a day and a night, she is considered as having non-menstrual vaginal bleeding (mustahada), so she fasts and prays. However, she must perform ablution for every obligatory prayer after its time enters, pray immediately, and be treated as a person with a continuous condition. There is no specific end limit for a woman's menstruation; it is possible as long as the woman is alive. 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 ruling of Islamic Law on a latecomer who joins the imam during the standing position of the first rakʿah but was unable to complete the recitation of al-Fātiḥah?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If a latecomer (masbuq) joins the prayer while the imam is standing, he should begin reciting Sūrat al-Fātiḥah immediately, without pausing to recite the opening supplication (duʿāʾ al-istiftāḥ) or the seeking of refuge (taʿawwudh). If the imam bows before he completes al-Fātiḥah, he follows the imam into the bow and leaves whatever remains of al-Fātiḥah — the imam bears it on his behalf.
It is stated in ʿUmdat al-Sālik (p. 47): "If a latecomer finds the imam standing and is confident that he has enough time to recite the taʿawwudh and al-Fātiḥah in full, he may do so. If he is uncertain, he should neither recite the opening supplication nor the taʿawwudh, but rather begin directly with al-Fātiḥah. If the imam bows before he completes it, he follows him into the bow — provided he had not already begun the opening supplication or the taʿawwudh. If he had begun either of them, he continues reciting al-Fātiḥah for as long as he spent on them." And Allah the Almighty knows best.