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 forgetting an integral of the prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Whoever forgets an integral (Rukn) of the prayer and remembers it before reaching the equivalent point in the subsequent unit (Rak'ah), must return to it (i.e., perform it) and complete his prayer, then perform the prostration of forgetfulness (Sujud al-Sahw) at the end of his prayer. However, if he remembers it after reaching the equivalent point in the subsequent unit, the Rak'ah in which the integral was forgotten is invalidated, and the current unit takes its place; he then completes a full Rak'ah to compensate and performs the prostration of forgetfulness.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.1/P.543): 'If he becomes certain at the end of his prayer, or after the Salam—provided the interval is not long according to custom and he has not stepped on an impurity—that he omitted a prostration from the final Rak'ah, he must perform it and repeat the Tashahhud, as his previous Tashahhud occurred before its proper place. If the omission was from a Rak'ah other than the final one, he must perform a full Rak'ah, because the deficient unit was completed by a prostration from the subsequent one, rendering the rest of that subsequent unit void.' And Allah the Exalted knows best.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
What fulfills the requirement of Suhoor?
Suhoor is fulfilled by eating even a single date or drinking a sip of water, anytime after midnight and before Fajr, with the intention of strengthening oneself for fasting.
