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.

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. 

I have been married for five years. My husband has two sons from his first marriage. Nevertheless, I took care of his children, and gave birth to a baby boy who is now three years old. Unfortunately, we keep fighting all the time; sometimes over his two sons and sometimes over his family. If I serve his family members and praise them, he treats me kindly. If I don`t, he turns my life into living hell. What should I do?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Spouses should live with each other on a footing of kindness and equity. In your case, constructive dialogue is the best course of action. We advise you to be patient, commit your affair to Allah and ask Him to help you. We also recommend that you seek the help of the people of goodness and make them fix things between you and your husband. If all attempts for reconciliation fail then go to court, but we remind you that a problem, which could be solved with a beautiful word, is no problem at all, so praise family and children and try your best to win their hearts. And Allah The Almighty Knows Best.

Is it permissible for one to masturbate in order not to commit fornication?

This is called committing the milder of the two evils such as eating a carcass in fear of death, and this happens when committing fornication is very likely to occur.