When does the time for the 'aqīqah lapse and pass?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the guardian was financially capable (mūsir) during the majority of the postnatal period (nifās) — which is sixty days — then the obligation of the 'aqīqah remains upon him until the child reaches the age of maturity (bulūgh). Once the child reaches maturity, the demand falls away from the father and those like him. At that point, it becomes Sunnah for the child himself to perform the 'aqīqah on his own behalf.
However, if the guardian was financially incapable (mu'sir) during the postnatal period, and then became financially capable after its expiry — that is, after sixty days — the 'aqīqah is no longer required of him. 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 valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.
Is it permissible for a sick person to pray while sitting on a chair?
All perfect praise be to Allah, The Lord of the Worlds It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.