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 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 permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.
If the bleeding ceases after 40 days following childbirth, but then returns intermittently during two days of fasting, what is the ruling?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Whenever the post-natal bleeding (Nifas) ceases and the woman is certain it will not return, she has become pure; therefore, she must perform the ritual bath (Ghusl) and resume praying and fasting. However, if the blood returns within fifteen days of its cessation and before sixty days have passed since the delivery, the ruling of Nifas applies once again. Consequently, any fasting or prayer performed during that interval of purity is rendered invalid; she must make up for the missed fasts of those days, but she is not required to make up for the prayers. And Allah the Exalted knows best.