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.
After our father had passed away, my brother and I stayed with our mother for twenty years and served her to the best of our effort. However, she asked our other brothers (3) to support her financially but they refused to pay her anything. As a result, she gave her share of the inheritance to me and my brother. What is the ruling of Sharia on this?
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 is recommended to give one`s children, males and females, equally. However, your mother is allowed to give one of them more than the others because he/she is needy or more dutiful to her than the others. And Allah The Almighty Knows Best.
Is buying shared land from someone who has taken possession of it considered halal or haram?
The shared land is possessed by the country i.e. for all people; therefore, it shouldn't be possessed/occupied save by it's guardian/owner permission,thusly it can't be possessed save by having owners' permission. Finally, buying it from a person who don't possess it is impermissible. And Allah Knows Best.
Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?
Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.