Is it religiously forbidden to build churches and to invite Christians to their religion, and if so, how do they practice their worship?

As for building churches in Islamic lands, this is one of the issues in which the legitimate ruler (wali al-amr) exercises ijtihad, or acts upon the opinion of trustworthy scholars in his country. It is not permissible for the Muslim ruler to allow the seduction of Muslims away from their religion by permitting proselytization for a religion other than Islam in an Islamic country.