What is the ruling on not fulfilling a vow?
A vow is a commitment towards Allah, The Almighty, and so, it should be observed as much as possible, and it is impermissible to take it lightly. Allah, The Exalted, Says –in commending the believers (What means): "(Because) they perform the vow and fear a day whereof the evil is wide-spreading." [Al-Insan/7].
Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?
Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. And Allah Knows Best.
A man has married a second wife and deprived the first from provision and overnight stay. He spent most of his time and wealth on his second wife. After sometime, the latter got sick and was diagnosed with breast cancer, which made him forsake her in bed and return to his first wife. What is the position of Sharia on this?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
It is forbidden for a woman to forsake her husband in bed without a lawful excuse since this is one of the mutual rights of spouses. When the wife abstains from making love to her husband without a lawful excuse, she is considered sinful. This is because the Prophet (PBUH) said: "If a woman spends the night deserting her husband's bed (does not sleep with him), then the angels send their curses on her till she comes back (to her husband)." [Agreed upon]. And Allah The Almighty Knows Best.
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.