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.
Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?
Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
What are the Sunnahs and etiquettes recommended for the person offering the Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
There are several Sunnahs and etiquettes that are recommended for the person offering the Udhiyah (sacrifice) to observe, including:
1. Refraining from Cutting Hair and Nails
It is Sunnah for the one intending to sacrifice to refrain from removing any hair or nails once the first ten days of Dhul-Hijjah begin.
The Prophet (peace be upon him) said: "When the ten days [of Dhul-Hijjah] begin and one of you intends to offer a sacrifice, let him not touch [remove] any of his hair or skin." [Narrated by Muslim].
If someone does remove any hair or nails, they have not committed a sin, and their sacrifice remains valid.
2. Performing the Slaughter Personally (or Witnessing it)
It is recommended for the person offering the sacrifice to slaughter the animal themselves. If they are unable to do so, they should witness the slaughter.
The Messenger of Allah (peace be upon him) said to Fatimah (may Allah be pleased with her): "Stand and witness your sacrifice, for indeed, with its first drop of blood, your [previous sins] are forgiven." [Narrated by Al-Bayhaqi and Al-Tabarani; it is classified as a weak (da'if) hadith].
3. Facing the Qiblah
The animal should be positioned to face the Qiblah at the time of slaughter, as the Qiblah is the most noble of directions.
4. Mentioning Allah's Name (Tasmiyah)
The slaughterer should say: "Bismillah ar-Rahman ar-Rahim" (In the name of Allah, the Entirely Merciful, the Especially Merciful). Even if one forgets to say it, the sacrifice is still permissible to eat.
Allah (Blessed and Exalted be He) says: "So eat of that [meat] upon which the name of Allah has been mentioned" [Al-An'am: 118].
It is also recommended to send blessings upon the Messenger of Allah (peace be upon him) and to say "Allahu Akbar" (Allah is the Greatest) after the Tasmiyah.
5. Supplicating for Acceptance
The slaughterer should pray for the sacrifice to be accepted by saying:
"O Allah, this is from You and for You, so please accept it from me." (Allahumma hadhihi minka wa ilayka, fataqabbal minni).
And Allah the Almighty knows best.
