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. 

What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?

Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.

What is the due amount of food in expiation for perjury? 

It is feeding ten indigent persons: 600 grams (for each) of the average food of your families such as rice, and it is permissible, according to Imam Ahmad Bin Hanbal, to give that amount in money if it was more useful to them.

My husband wanted to sell a piece of land that was his own, but his father insisted that he transfer the land in his (the father’s) name so that he could sell it at a higher price. Then, my husband and his father would split the price. After my father-in-law sold the land, he denied everything and refused to acknowledge my husband’s right. My father-in-law passed away a year ago, and my husband’s brothers divided the inheritance, refusing to acknowledge that this land was a trust held by their father for my husband until it was sold. Are they sinful for knowingly denying that the land belongs to my husband, and what is the ruling on praying against them?