Why was it called a world war if every country in the world was not involved?

It's a war for control of the world. ... The Americans, on the other hand, in 1914-17 usually called it the European War. Once the United States joined the war, of course, the American media could no longer refer to it as a European war: so it became the World War. That was the first large-scale use of the term in English.

separation of church and state? not sure what you mean.