Is it permissible to build a mosque in a village in America where there is no mosque and Muslim families live?

The basic rule is the permissibility of building mosques in towns and countries, and their construction is among the greatest acts of worship to Allah. Building a mosque for a single Muslim family in a village depends on balancing benefits and harms. If it will become a platform for Da'wah (inviting to Islam) and Muslims will increase because of it, then its construction is recommended. However, if it remains deserted, its construction might be a waste of money, and spending the money on another mosque would be more appropriate.