If you are interested in what founding fathers meant by America being a Republic, check out "The Federalist Papers". One of them by James Madison explains it.As for the US being founded on Christianity, I think that there were two reasons why Church and State were separated (there are many reasons why it should be that way, but I think only 2 really mattered back then). The first was because the a lot of visionaries wanted the US to become a new Roman Republic, and the other is because European nations didnt have a separation. The US was trying to show emphatically how uneuropean they were. Im not American and so I wasnt raised on US history so these points could be way off. If they are, please tell me.
Here it is: