Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
What is the semi-circular structure attached to the Holy Kabah?
The semi-circular structure attached to the Holy Kabah is Hijr Al-Kabah (is a low wall originally part of the Kabah) and passing behind it is an obligation while making Tawaf because it is a part of the Holy Kabah. And Allah Knows Best.
What is the ruling on someone who prays but does not fast, without a valid excuse?
Fasting is one of the pillars of Islam, and a Muslim's faith is incomplete if they neglect the obligation of fasting while being physically capable of observing it.
What is the ruling of Islamic Law on the colored discharges that appear one or two days before the menstrual cycle?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Colored discharges carry the same Islamic ruling as blood, whether they appear at the beginning or the end of the menstrual period. This remains true even if the discharge is intermittent—appearing for some days and stopping for others before returning—provided that the total duration does not exceed fifteen days nor fall short of a day and a night (24 hours). This is because the minimum duration of menstruation (Hayd) is one day and a night, while its maximum duration is fifteen days. Furthermore, the minimum period of purity (Tuhr) between two menstrual cycles is fifteen days, and there is no maximum limit for it. And Allah the Exalted knows best."