What is the Islamic ruling on eating from the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is recommended (mandūb) to eat from the 'aqīqah, unless it was vowed (mandhūrah). If the 'aqīqah was made as a vow, then it is prohibited to eat from it, and it becomes obligatory to distribute the entirety of it in charity to the poor. And Allah Almighty knows best.
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.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
If a father stops his daughter from getting married, is it permissible for her to conclude the marriage contract herself?
It is permissible for the father to stop his daughter from getting married if there was a lawful reason for that, and she isn`t allowed to conclude the marriage contract without her guardian. However, if her father denied her right in getting married for an unlawful reason, then she should go to court.