Is it permissible to pray in a mosque above which a family residence has been built, and is it permissible to live above a mosque?

A mosque becomes a waqf (endowment) as soon as it is built and permission is given for prayer within it. Its ownership is relinquished by the endower, and it cannot be reclaimed except for its benefit. As for whether the endower stipulates the right to build above or below it, there is a difference of opinion: The Malikis prohibited building above it but permitted it below, while the Hanbalis prohibited benefiting from the surface below a mosque and reversed the ruling (i.e., permitted above but not below), and Abu Yusuf permitted building both above and below it. The correct view is that it is permissible to build above or below it if that was the intention of the endower, and prayer in a mosque above or below a dwelling is valid without dispute.