Is it permissible for a woman who is in her `Iddah (waiting period) due to the death of her husband to go out and mix with non-Mahrams(Marriageable men)?
A woman in such a situation is only allowed to leave her house for a sound reason such as visiting the doctor, and she is only allowed to mix with her Mahrams(Non-Marriageable kin) since it is permissible for a woman, whether in her `Iddah, or not, to mix with her husband and Mahrams. However, she is allowed to accept condolences, and answer inquiries about her situation after such a calamity.
Is it permissible for the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible as long as his Awrah(private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best
What is the semi-circular structure abutting the Holy Kabah?
It is the Black Stone of the Holy Kabah, and one should pass from behind it while offering Tawaf(circumambulation) because it is part of the Kabah.
If the Prophet (PBUH) was an Arab citizen in 2009, born in an Arab country ruled by an Arab ruler, saw what was happening to Gaza, what would he (PBUH) have done?
All perfect praise be to Allah, The Lord of The Worlds. May His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Had the Prophet (PBUH) been amongst us, Muslims would have supported him, and then he would do whatever pleases the heart of every Muslim. And Allah The Almighty Knows Best.