Is it permissible for a financially capable woman to pay the Zakat to her sons or one of them?
It is permissible for a mother to give her children from zakat if they are eligible to receive it, even though she is obligated to provide for them. This is based on the saying of the Prophet Muhammad (PBUH) regarding Zainab, the wife of Abdullah Ibn Mas'ud (may Allah be pleased with them): "Your husband and your children are more deserving of your charity" [Al-Bukhari]. 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.
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 permissible for us to sever ties of kinship if our blood-relatives` gatherings/meetings involve acts of sin?
Observing kinship ties is obligatory, and paying your blood-relatives a visit causing their sinful acts to be hindered , then you should do so. However, if their sinful acts continue while you are at their gathering and they didn't respond positively, then observing kinship ties via telephone and the like will suffice in this case. And Allah Knows