I am a Jew by tradition who does not believe in any gods. Regardless of whether or not you share my views, you should understand that people such as me are citizens and deserve a say in government as well. To do so otherwise is to remove me of my freedom.
Church and state should be separated in the sense that there can be no compulsion to follow a certain religion or punishment for not doing so or for not believing anything. However, we have to watch out about getting ridiculous about it. Certainly, there are values that most world religions share that are helpful for political thinking and making it ethical.
No. The church played an important role in the development of the United States, and it should be allowed to continue playing a role in state affairs. That is not to say that the state's decisions should be made to reflect the views of the church, but there should be a healthy respect between church and state.