Is it permissible to fast on behalf of the dead who died owing missed fast to make up?
His relative should fast on his behalf, and it is permissible for the guardians to give permission to non-relatives of the dead to fast on his behalf as well. And Allah Knows Best.
Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.
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. And Allah Knows Best.
What is the ruling of Sharia on marrying a Jewish woman, dealing with the Jews, and going to Israel?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is allowed for a Muslim to marry a Jewish or a Christian woman provided that this doesn`t affect his religion. As for dealing with the Jews who are outside Palestine, it is the same as dealing with the Christians; it is permissible as long as it doesn`t harm Islam. As for dealing with the Jews who are inside Palestine, the ruling differs depending on the persons themselves and the situations. By the end of the day, a believer`s heart leads him/her to what is good. And Allah The Almighty Knows Best.