Is it permissible to give my zakat to my grandson who is studying at university, while I am living abroad and my money is in my home country? Also, is it permissible to assign my father the responsibility of distributing the zakat to the people in my home country?
It is permissible to give zakat to a son whom his father is supporting if he is an adult and in good health, because his father is not obligated to support him, making him one of the poor among the Muslims. However, the student who may receive zakat is one who is diligent in seeking beneficial knowledge for the Muslims and is religious. Zakat should be paid in the country where the money is located, and appointing your father to distribute the zakat in the country where the money is is the correct approach. And Allah Knows Best.
I am an author, and I have books stored with me. Is it permissible to pay my zakat in the form of books containing beneficial knowledge for poor students, such as chemistry and mathematics, or religious books that spread Islamic sciences?
Zakat on wealth must be paid in cash from the wealth itself. Therefore, you should pay your zakat in monetary form so that the poor can purchase what they need. And Allah Knows Best.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is it permissible for a Muslim woman to marry a Christian man?
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.
It isn`t permissible for a Muslim woman to marry a Christian and such marriage, from an Islamic position, is invalid. And Allah The Almighty Knows Best.