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.
Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?
The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.
What is the ruling on Zakat al-Fitr?
Zakat al-Fitr is obligatory upon every Muslim for themselves and for those they are financially responsible for, provided they possess wealth that is surplus to their and their family's needs on the night and day of Eid.
Ibn Umar reported: "The Messenger of Allah ﷺ made Zakat al-Fitr obligatory—one sa‘ (measure) of dates or one sa‘ of barley—upon every Muslim, whether slave or free, male or female, young or old." [Narrated by Al-Bukhari]
Its estimated amount is approximately 2,500 grams of wheat or rice, and the General Iftaa` Department issues an annual ruling specifying its monetary value.
Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.