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 the prayer of one who said "Subḥāna Rabbiya al-ʿAẓīm" in prostration (*sujūd*) and forgot to correct it?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Saying “Subḥāna Rabbiya al-ʿAẓīm” in bowing (rukūʿ) and “Subḥāna Rabbiya al-Aʿlā” in prostration (sujūd) is one of the hayʾāt (non-essential sunnahs) of the prayer. Whoever omits it, whether deliberately or by forgetfulness, or replaces it with another remembrance (dhikr), his prayer is valid and he does not perform sujūd al-sahw. Shaykh al-Islām Imam al-Nawawī (may Allah have mercy on him) said: “Our school holds that one does not prostrate for omitting the audible or silent recitation, the tasbīḥ, and the rest of the hayʾāt.” [al-Majmūʿ, Vol.4/p.127]
If he performs sujūd al-sahw for something that does not call for it, his prayer is invalidated, because he introduced a prostration of forgetfulness without a cause, and he must repeat the prayer. The exception is one who did so out of forgetfulness or ignorance, whether because he recently entered Islam or because he lives far from scholars; he is excused and his prayer is not invalidated.
It is stated in Mughni al-Muḥtāj (Vol.1/p.417): “It is stated in al-Anwār: If he does something that does not call for sujūd al-sahw, thinking that it does, and then prostrates, his prayer is not invalidated if he is ignorant because he recently entered Islam or because he is far from scholars.”
Since this issue is hidden from the laity, as it is among the subtleties of knowledge, and the laity are excused for ignorance of whatever is of such a nature, and their act of obedience is not invalidated because of it, it may be said that the prayer of one who has not acquired knowledge of the issue is not invalidated. As for after knowing it, the prayer is invalidated.
Whoever realizes while still in the prayer that his prostration was out of place, it is sunnah for him to perform sujūd al-sahw. And Allah Almighty knows best.
What is the ruling of Islamic Law on performing ṭawāf on the upper floors of al-Masjid al-Ḥarām, given that these floors are situated above the level of the Ka‘bah, and that the one performing ṭawāf passes by certain barriers, such as pillars and walls, during the ṭawāf?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
There are numerous conditions for the validity of ṭawāf (circumambulation around the Ka‘bah), among them: that the one performing ṭawāf be inside the Masjid (al-Masjid al-Ḥarām) — even if the Masjid has been expanded, so long as the expansion does not extend out into al-ḥill (land outside the sanctuary boundaries). It suffices for the ṭawāf to be performed in the airspace of the Masjid or upon its roof, even if that roof is higher than the Ka‘bah (the House) itself.
Al-Khaṭīb ash-Shirbīnī (raḥimahullāh) said: "It [ṭawāf] is valid upon the roof of the Masjid, even if the roof of the Masjid is higher than the House — just as prayer [is valid] upon Mount Abū Qubays despite its elevation above the House. This is the relied-upon (mu‘tamad) position." [Mughnī al-Muḥtāj, Vol.2/P.246]
The validity of the tawaf isn`t affected by the pillars and walls standing between the one performing ṭawāf and the House, since the condition is only that the person performing ṭawāf be within the boundaries of the Masjid and outside the boundaries of the Ka‘bah itself.
Ash-Shirbīnī said: "It [ṭawāf] is valid inside the Masjid, even if it is expanded, and even if a barrier stands between the one circumambulating and the House — such as a water-supply structure (saqāyah) or pillars (sawārī)." [Mughnī al-Muḥtāj, Vol. 2/P.246]
Accordingly, ṭawāf performed on the upper floors is valid, and the presence of barriers such as pillars and walls during the ṭawāf does not affect its validity. And Allah, the Exalted, knows best.
What is the ruling on swimming while fasting?
Swimming while fasting is disliked (makruh) due to the risk of water entering the body cavity (jauf) through the nose, ears, or mouth, which would break the fast.
Ramadan is a month of tasbeeh (glorifying Allah), not Sibaha (swimming).