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 ruling on the intention of fasting, where is its place, and when is its time?
The intention is a pillar of acts of worship; it is essential, and worship is not valid without it.
Its place is in the heart, and verbalizing it is recommended so that the tongue reminds the heart. Its meaning is to be determined to abstain from nullifiers of fasting during the upcoming day with the intention of worship and obedience to Allah Almighty. This meaning is naturally present in every Muslim on every night of Ramadan, so there is no need for obsessive doubts. If one says, "I intend to fast tomorrow for the sake of Allah," it removes any doubts.
Its time is from after sunset until before the true dawn.
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 wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.
