Is it permissible for a woman to perform the obligatory prayer immediately after the adhan and before the Iqamah is performed in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible for a woman to perform the obligatory (Fard) prayer immediately after the Adhan (call to prayer) and before the Iqamah (call to commence prayer) is performed in the mosque. And Allah the Exalted knows best.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
What do you say about someone who stays up all night on Laylat al-Qadr but misses Fajr prayer?
Such a person has deprived themselves of a great reward. Performing obligatory acts is more beloved to Allah than voluntary acts. Fajr prayer is an obligation, and performing it in congregation is equivalent to worshiping for the entire night. So how can someone neglect it while striving for voluntary prayers?!
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.