Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
What is the ruling of Sharia when husband kicks the wife out of his house without a lawful excuse? Moreover, in such case, when she stays at her parents's house for several months, is she allowed to claim maintenance through a Sharia court?
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 to kick wife out of house save for a valid reason since Almighty Allah Says (What means): "O ye who believe! Ye are forbidden to inherit women against their will. Nor should ye treat them with harshness, that ye may Take away part of the dower ye have given them,-except where they have been guilty of open lewdness; on the contrary live with them on a footing of kindness and equity. If ye take a dislike to them it may be that ye dislike a thing, and God brings about through it a great deal of good." [An-Nisa`/19]. In addition, it is the duty of the husband to provide for his wife and children in kindness, and this includes food, garment and residence. Moreover, dialogue and supplication are the best means for solving marital problems; however, the wronged party may resort to court. And Allah The Almighty Knows Best.
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.
What is the ruling of Sharia on marrying the maternal niece of one`s wife?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
One may not combine in marriage a woman and her paternal aunt, or a woman and her maternal aunt, as stated the Prophet (PBUH). And Allah The Almighty Knows Best.