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.
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].
If a woman makes a vow to slaughter a sheep, and her husband is the one who buys it for her from his own money, and he says: "It is for you until you fulfill your vow with it," Is this permissible, or must she buy it herself from her own money?
If her husband gave her the sheep as a donation for the puprose of fulfilling the oath she made and was slaughtered by the wife or the husband on her behalf then the vow she made is fulfilled. And Allah Knows Best.
Is it true that whatever is dry is pure even if there was impurity on it?
The impure material object does not soil (make impure) anything else unless the impurity is wet and transferable. But, if the impurity is dry or non-transferable, then there is no problem. Fuqaha has stated that: There is no disagreement between Muslim scholars that when a dry impurity touches something dry it does not make the latter impure.