It does not seem that there is any clear evidence that it is haram for Muslims to enter churches. But at least it is makruh to enter churches unnecessarily, because the fact that the angels and the Prophet did not enter the house in which there were images indicates that it is makruh. Moreover this being makruh may reach the level of being haram if entering the church will lead to any bad consequences. For more, please see the detailed answer.

A Muslim man can marry a Chrisitan or a Jewish woman. But if the woman who wants to marry a Muslim man is not one of the people of the Book, then it is not permissible for a Muslim to marry her.