Is a husband entitled to ask his wife to furnish the house from her dower (mahr), and is it obligatory for the wife to do so if the custom in her country dictates that the woman furnishes the house from her dower?

The Mahr (dower) is an exclusive right of the wife; she may dispose of it as she wishes. She is not obligated to furnish the marital home, as there is no text that compels her to do so. If she does, it is considered a voluntary act on her part. Furnishing the home is the husband's duty; he is responsible for providing all necessary furnishings, belongings, and tools, as this falls under his obligatory financial support for his wife.