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 on the follower (*maʾmūm*) reciting Sūrat al-Fātiḥah behind the imam?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
In our school of Islamic thought, the Shāfiʿī school, reciting al-Fātiḥah is obligatory in every rakʿah of the prayer for the imam, the follower (maʾmūm), and the one praying individually (munfarid), because it is one of the pillars (arkān) of the prayer. Whoever does not perform it, his prayer is invalid, whether the prayer is silent (sirriyyah) or audible (jahriyyah), based on the saying of the Prophet (peace and blessings be upon him): “The prayer of the one who does not recite the Opening of the Book (Fātiḥat al-Kitāb) is invalid.” Agreed upon.
It is stated in ʿUmdat al-Sālik, one of the books of the Shāfiʿī school: “He recites al-Fātiḥah in every rakʿah, whether he is the imam, the follower, or the individual worshipper.”
The jurists of the other schools hold a different opinion, which was previously explained in Fatwa no. (
3169); please refer to it. And Allah Almighty knows best.
What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.