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 a person who insists on praying in a specific spot and becomes angry if someone else prays there?
ruling on a person who persists in praying in a specific spot and becomes angry if someone else occupies it
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Our Master the Prophet ﷺ forbade a man from habitually claiming a specific spot in the mosque as a camel claims its place (to sit); scholars consider this to be among the disliked matters (Makruhat). It is therefore obligatory to advise this individual that whoever arrives at a spot first has the most right to it. And Allah the Exalted knows best.
Is it a condition for the mosque where I‘tikaf is performed to hold Jumu‘ah prayers?
No, it is not a condition for the mosque where I‘tikaf is performed to have Jumu‘ah prayers. However, if a person vows to perform continuous I‘tikaf, and Jumu‘ah occurs within that period, then they must observe I‘tikaf in a mosque where Jumu‘ah is held so that they do not break their continuity by leaving for Friday prayer.
What is the ruling on one who wiped over his leather socks (*khuff*) while resident and then traveled, or wiped while traveling and then became resident? And likewise, what is the ruling on one who incurred a minor ritual impurity (*ḥadath aṣghar*) while resident, then traveled and wiped while traveling?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Whoever wipes over his leather socks (khuffayn) while resident and then travels, or wipes while traveling and then becomes resident, before a day and a night have passed in both cases, completes the wiping period of a resident. If he wipes while resident and then travels after a day and a night have passed, he must remove the socks, because the period has ended. Likewise, if he wipes while traveling and then becomes resident after a day and a night have passed, he must remove them as well.
Whoever breaks his wuḍūʾ while resident and then wipes while traveling takes the ruling of a traveler as regards the duration of wiping, so long as he does not become resident. It is stated in ʿUmdat al-Sālik wa ʿUddat al-Nāsik (Vol.1/p.15): “If he wipes over both [socks] or one of them while resident and then travels, or wipes while traveling and then becomes resident, or doubts whether he began the wiping while traveling or while resident, he completes only the wiping period of a resident. But if he broke his wuḍūʾ while resident and wiped while traveling, he completes the period of a traveler, whether or not the full time of a prayer had passed over him while resident.” And Allah Almighty knows best.