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.
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.
I can`t afford to get married, what should I do to curb my sexual drives?
You should offer a lot of voluntary fasting, keep busy with useful and permissible acts and make supplication to Allah, The Exalted.
What is the ruling on discharges two or three days before the expected period of menstruation and the light-colored blood accompanying it? Must the woman abstain from prayer during this period?
If the total duration of these blood-tinged discharges reaches a day and a night (24 hours) or more, it is considered menstruation. If their total does not exceed 24 hours, it is not considered menstruation but is irregular bleeding (dam al-fasad). Each woman has specific cases for which she should ask the scholars. And Allah the Almighty knows best.