What is the ruling of Islamic Law on performing prayer on the upper floors of al-Masjid al-Ḥarām?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Facing the actual structure of the Ka‘bah (‘ayn al-Ka‘bah) is one of the conditions for the validity of the prayer. The scholars have clarified what is meant by "the actual structure of the Ka‘bah."
Imam ash-Sharwānī (raḥimahullāh) said: "What is meant by its ‘ayn (actual structure) is its physical body, or the airspace directly aligned with it — if the person praying is not inside it. But if he is inside it, then the airspace alone does not suffice; rather, the actual physical structure must be faced, such that even if he faces a projecting part of it measuring roughly two-thirds of a dhirā‘ (cubit) or more, this would be sufficient." [Ḥāshiyat ash-Sharwānī ‘alā Tuḥfat al-Muḥtāj, Vol.1/P.484]
Sheikh al-Qulyūbī (raḥimahullāh) said: "Unlike one who prays outside it — i.e., outside the Ka‘bah — for him the airspace (directly above it) suffices, even if he is higher than it, or even if he is at the location where it (hypothetically) has been demolished." [Ḥāshiyat al-Qulyūbī ‘alā Sharḥ al-Minhāj, Vol.1/P.154]
Accordingly, the prayer is valid on the upper floors of al-Masjid al-Ḥarām, even though these floors are higher than the roof of the Ka‘bah itself. And Allah, the Exalted, 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.
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).
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.