Is it permissible to complete the construction of a mosque built on land usurped from the state without a permit, and is prayer in it valid, and is it considered a sin for the one who built it?

As long as there is evidence or an indication that the land is designated by the state for another purpose, it is not permissible to continue building until the state has been consulted and a building permit obtained. If it is confirmed that it is designated for a specific entity, then it is not permissible to continue and what has been built must be demolished, unless the state grants permission. If it is not designated for anyone, then it is permissible to continue with the construction.