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.
Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?
Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.
Which is better during the day in Ramadan: reciting the Quran or performing voluntary prayers?
A Muslim should establish a daily schedule for reciting the Quran in Ramadan.
Once they have completed their daily portion (known as a wird or hizb), they can engage in other acts of worship, including voluntary prayers (nawafil). Prayer itself is called "Quran", because a significant part of it involves reciting the Quran.
Allah says: "BE CONSTANT in [thy] prayer from the time when the sun has passed its zenith till the darkness of night, and [be ever mindful of its] recitation at dawn: for, behold, the recitation [of prayer] at dawn is indeed witnessed [by all that is holy]." [Al-Isra`/78]
How does the person praying perform the prostration (Sujud)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is an act of Sunnah for the person praying to descend for prostration (Sujud) by placing their knees first, then placing their hands on the ground, and then placing their nose and forehead simultaneously. It is obligatory that the toes of the feet be on the ground, directed towards the Qibla. And Allah the Exalted knows best.