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.
What is the ruling if someone wipes his head then shaves it - must he repeat it?
If a person performing ablution shaves his head after wiping it during ablution, he is not required to re-wipe his head or repeat the ablution. And Allah the Almighty knows best.
Is a menstruating woman obliged to pray during menses, and should she make up missed prayers?
All perfect praise be to Allah, The Lord of The Worlds A menstruating woman is prohibited from prayer during her menses, and she isn`t obliged to make up missed prayers. And Allah Knows Best.
How is the meat of the 'aqīqah to be distributed?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the 'aqīqah is a recommended one (mandūbah), it is obligatory to give some portion of it in charity to the poor — even if the amount is small — with the minimum being approximately half a kilogram of meat.
The most preferable manner of distribution is to divide it into three equal portions, as with the uḍḥiyyah:
One third for the guardian and his household to eat from
One third to be given in charity to the poor
One third to be gifted to friends and neighbours, even if they are wealthy
It is furthermore more preferable to send the food to the poor already cooked, rather than inviting them to come and eat. And Allah Almighty knows best.