What are the conditions that must be met for the 'aqīqah to be valid?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is like the recommended uḍḥiyyah in terms of the type of animal, its age, and its required characteristics — since it is a recommended slaughter and therefore resembles the uḍḥiyyah in its rulings.
It is agreed upon without any difference of opinion that the 'aqīqah is not valid with any animal other than livestock (al-na'am — camels, cattle, and sheep). Likewise, an animal with a disqualifying defect — such as obvious illness, lameness, or blindness in one eye — does not suffice, as has previously been explained in the rulings of the uḍḥiyyah. And Allah Almighty knows best.
What is the ruling on a young man and a young woman having a love relation for the purpose of getting married?
It is forbidden for a man and a woman to have any kind of relation whether for marriage, or not because it leads to committing sin. Such relations include: private meetings, mixing, gazing, and seclusion (Khulwa). Accordingly, one who is sincere in his intentions should go to the woman`s guardian and ask for her hand in marriage.
What is the Islamic ruling on smearing the head of the newborn with the blood of the `Aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (makrūh) to smear the head of the newborn with the blood of the 'aqīqah, as this is a practice that belongs to the customs of the pre-Islamic era of ignorance (Jāhiliyyah). What is Sunnah instead is to anoint the newborn's head with saffron or another pleasant fragrance. And Allah Almighty knows best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.