Which is better and more rewarding: building a mosque next to the house after demolishing the old prayer hall, or building a house and housing a needy family in it?

Both actions contain great good and reward. If one is unable to perform both, then one should consider which is more urgent. If there is a family in need of shelter, and the neighborhood is not in dire need of a mosque, then building the house takes precedence. Otherwise, the mosque is more deserving. A prayer area (musalla) established in a house is not considered a mosque unless it is built in the form of a mosque and a general call to prayer is issued therein. In that case, it is considered an endowment (waqf), and it is not permissible to build anything other than a mosque in its place. The one who demolished it must rebuild it.