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.
Should a minor fulfill his vow?
The vow of a minor is countless because he isn`t required to meet the Sharia rulings at such an age, and it is desirable for him to fulfill that vow once he reaches puberty.
Is it permissible for a person who has to make up for missed fasts to fast six days of Shawwal (the month directly after Ramadan) before making up for the missed fasts?
Yes, it is permissible for him/her to do so, but it is better that they make up for missed fasts first. And Allah Knows Best.
My father passed away before my grandfather. Am I entitled to any share of my grandfather`s inheritance?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
According to Islamic courts, you are entitled to what is called obligatory bequest (The distribution of estate to grandchildren who has either lost a parent before the death of the grandparents). Therefore, if your grandfather left such bequest for you, then take that share or else it is more prudent to take nothing. And Allah The Almighty Knows Best.