What is the semi-circular structure attached to the Holy Kabah?
The semi-circular structure attached to the Holy Kabah is Hijr Al-Kabah (is a low wall originally part of the Kabah) and passing behind it is an obligation while making Tawaf because it is a part of the Holy Kabah. And Allah Knows Best.
What is the ruling of Islamic Law on performing the Witr prayer after the Adhan for Fajr prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The time for Witr prayer begins after the ‘Ishā' prayer and ends with the rising of true dawn (al-fajr aṣ-ṣādiq). If a Muslim performs it at any point within this window, it counts as performed on time.
It is also recommended to make up a missed Witr prayer at any time — whether before or after performing the Fajr prayer, or at any other time of day. On the authority of Abū Sa‘īd al-Khudrī (raḍiyallāhu ‘anh), the Messenger of Allah ﷺ said: "Whoever falls asleep and misses the Witr prayer, or forgets it, let him pray it when he remembers, or when he wakes up." (Related by at-Tirmidhī)
Shaykh al-Islām, Imam Ibn Ḥajar al-Haytamī (raḥimahullāh), says: "The time for Witr prayer is between the ‘Ishā' prayer and the rising of dawn, based on the authentic ḥadīth to this effect. If this time has passed, it is permissible for him to make it up (qaḍā') afterward." [Tuḥfat al-Muḥtāj]. And Allah, the Exalted, knows best.
Does the fast become invalid if water from rinsing the mouth reaches the stomach while performing ablution?
If water reaches the stomach without the fasting person exceeding normal rinsing or being excessive, their fast remains valid.
However, if they exceed the normal practice or exaggerate in rinsing, causing water to enter the stomach, their fast is invalid.
This is because excessiveness in rinsing is prohibited for a fasting person, as the Prophetﷺ said: "Exaggerate inhaling water during ablution, except when you are fasting." [Narrated by the Four Imams]
Transgression (Ta‘addi) refers to rinsing the mouth more than three times, while exaggeration (Mubalaghah) includes gargling, drawing water deep into the nasal passages, or filling the mouth with water in an unusual manner.
What is the ruling on making up the regular *rawātib* (sunnah) prayers together with a missed obligatory prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to make up (qaḍāʾ) a missed obligatory prayer (farḍ). As for the timed supererogatory prayers (al-sunan al-muʾaqqatah) or the regular rawātib prayers, it is recommended (mandūb) to make them up, even if a long time has passed. Ibn Ḥajar (may Allah have mercy on him) said in his Fatāwā: "It is established in our school that it is sunnah to make up the timed voluntary prayers, by night or by day, even if congregation is not prescribed for them, whether much time has passed or little."
Accordingly, it is recommended to make up the sunan together with the obligatory prayer. And Allah Almighty knows best.
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Note on terminology: Al-nawāfil al-muʾaqqatah (timed voluntary prayers) refers to supererogatory prayers tied to a specific time or cause, such as the rawātib (regular prayers before and after the obligatory ones), Duha, and the like. The ruling given here reflects the Shāfiʿī position.