Is a wife considered sinful if she asked for divorce because her husband married another woman?
A second marriage is lawful, and so it is impermissible for you to ask for divorce because of that. If you are certain that you won`t be able to deliver Allah`s rights and those of your husband`s , then it is permissible for you to ask for Khul`a (Divorce on the demand of the wife). However, you should exercise patience since after difficulties, there is easiness by the will of Allah.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
What husband's stand should be, if his wife disagrees with his mother?
Both the mother and the wife have rights on you (Questioner); therefore, you are obliged to treat both justly, resort to wisdom to please both and intiate reestablishing cordial relations among them. And Allah Knows Best.
A woman has asked her husband for Khulu`, her gold, deferred portion of the dowry and furniture. Is she entitled to that, knowing that her husband doesn`t want to divorce her?
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.
Khulu`* can`t takes place save before a judge of Sharia and he has the authority to make the suitable decision in this matter. And Allah The Almighty Knows Best.
* Khulu' is when parties agree to separate by way of consent, usually upon terms such as the wife agreeing to repay her Mahr (dowry) to the husband upon him agreeing to grant Talaq. The iddah period (waiting time after a divorce) of a woman who seeks a khula, is one menstrual cycle or one month if she is post-menopause i.e. ceased menstruating. This is to ensure she is not pregnant. This differs from when a man gives a talaq; the iddah period is three cycles or three months.