Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?

Yes, it is valid as long as it is registered at the court.

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 allowed to shave my beard to join the army taking into consideration that I can`t find a job?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

The army should be joined in preparation for Jihad (Fighting in the cause of Allah), so if Jihad contradicts with growing a beard then it is allowed to shave it. And Allah The Almighty Knows Best.  

If a woman makes a vow to slaughter a sheep, and her husband is the one who buys it for her from his own money, and he says: "It is for you until you fulfill your vow with it," Is this permissible, or must she buy it herself from her own money?

If her husband gave her the sheep as a donation for the puprose of fulfilling the oath she made and was slaughtered by the wife or the husband on her behalf then the vow she made is fulfilled. And Allah Knows Best.