Is it permissible for the big brother to force his sisters to wear Hijjab(Islamic wear) if their father didn`t do his part in this regard ?
The father`s attention should be drawn gently and politely, and the sisters should also be reminded with good words since Allah, The Almighty, says: “O ye who believe! Save yourselves and your families from a Fire whose fuel is Men and Stones.”{Al-Tahreem/6}.
Is it incumbent on a family to provide for its old handicapped son and take care of him?
The family and relatives- e.g.brothers- of such a person are obliged to spend on him and take care of him if he didn`t have money of his own.
Is Zakah due on the orphan`s money?
Yes, Zakah is due on the money of the orphan.
Generally speaking, I`m dutiful to my mother and opt for obeying her. However, she chose a certain girl to be my future wife, but I`m not pleased with her choice although that girl comes from a good family and enjoys good character. Should I obey my mother or choose another girl that lives up to my expectations?
Praise be to Allah the Lord of the Worlds.
One must obey their parents in whatever is in compliance with the teachings of Sharia and within one`s capacity. However, you aren`t to blame for not marrying that girl, but it is better that you tell your mother about that and it is preferable that you perform Istikharah prayer. And Allah The Almighty Knows Best.