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.
What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?
All perfect praise be to Allah, The Lord of The Worlds. Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.
Is it permissible for a religious young Muslim woman to love a young man for Allah`s sakes?
Such love between the two sexes is from the devil`s evil suggestions, and a pure Muslim woman should beware of such a matter, and she shouldn`t mix with non-Mahrams (Marriageable ).