What is the ruling on performing the obligatory prayer immediately after the commencement of the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible to perform the obligatory prayer (Fard) immediately after the commencement of the prayer time. As the Adhan (call to prayer) serves as a sign that the time has entered, it is permissible to pray as soon as the Adhan begins. However, it is recommended (Mustahabb) for whoever hears the Mu’adhin to repeat what he says. If the Adhan occurs while one is already engaged in prayer, he should repeat the words of the Mu’adhin after he has completed his prayer. And Allah the Exalted knows best.
What is the ruling on performing istinja' with perfumed tissues or a tissue moistened with water?
Performing istinja' with perfumed or moistened tissues is not sufficient if they are not dry, due to the moisture on them reaching the impurity, which increases its spread rather than reducing it. Then, to remove the impurity, one must use pure water. And Allah the Almighty knows best.
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 the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.