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 it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
What is the ruling on someone who eats or drinks thinking that the night is still present, then realizes that dawn has broken?
Whoever eats or drinks thinking that the night is still present, then later discovers that dawn has broken, must refrain from eating and drinking for the rest of the day out of respect for the sacred month. However, they must make up that day after Ramadan, and there is no sin upon them.
What is the age of the Aqiqa or the Udhiyah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The minimum age for a sacrificial animal (Udhiyah) and the birth sacrifice (Aqiqa) is as follows:
Camels: Five years old, entering their sixth year.
Cattle and Goats: Two years old, entering their third year.
Sheep: One year old, entering their second year; however, it is permissible for a sheep to be six months old provided it is large in size and plump.
And Allah the Exalted knows best.