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.
What is the ruling on eating or drinking during the first Adhan?
It is permissible to eat and drink during the first Adhan because it takes place before the break of dawn. The purpose of this Adhan is to notify Muslims of the approaching dawn so they can prepare to stop eating when they hear the second Adhan.
What is the ruling on attending relatives` parties held in public halls, or hotels since if we don`t, we will be subjected to their admonition?
If such parties involve mixing between men and women, or forbidden acts such as listening to songs with sinful lyrics, then attending them is forbidden from the view point of Sharia since people`s admonition is nothing compared to Allah`s, The Almighty`s, wrath.
What is the Islamic ruling on breaking the bones of the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah not to break the bones of the 'aqīqah. Rather, each bone should be separated at its joint — as a good omen and expression of hope for the soundness and wholeness of the newborn's limbs. However, if one does break the bones, it is not considered disliked (makrūh) — it is simply regarded as contrary to what is preferable (khilāf al-awlā). And Allah Almighty knows best.