Does the 'aqīqah count as valid if it is slaughtered before the seventh day from the birth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The time during which it becomes permissible to slaughter the 'aqīqah begins from the moment the newborn is fully delivered from its mother's womb.
If the animal is slaughtered prior to the birth, it does not count as an 'aqīqah — it is simply considered an ordinary sheep slaughtered for its meat.
And Allah Almighty knows best.
What is the ruling on forgoing the sacrifice (uḍḥiyah) for one who is financially able to offer it?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
It is disliked (makrūh) for one for whom the uḍḥiyah (sacrifice) is recommended (Sunnah) to forgo offering it, on account of the scholarly disagreement regarding whether it is obligatory. And Allah, the Most High, knows best.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
Is it permissible to sacrifice imported livestock (Such as Romanian, Australian, etc.)?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
As long as the sheep meets the prescribed Sharia age and is free from disqualifying defects, it is valid for sacrifice regardless of its country of origin. Therefore, it is permissible to offer sacrifices from various sources, such as: Romanian, Australian, Spanish, Indian, Sudanese, local (Baladi) livestock, and others. And Allah the Almighty knows best.