Depends on how much you want to stretch the term "democracy".

The Netherlands have a kind-of democracy during Philip II's reign. But the US was most definitely unique in terms of size, as well as the method of governance, namely federalism.

The UK was definitely tilted more in balance of a parliamentary democracy, but not really there yet, considering the strength of the aristocracy and such.

So, in essence, no. The US was not the only democratic state. Additionally, I believe that the line you quoted is more saying that Democracy as an idea of governance by the people will not perish from the earth. Not just the US

sort of. This is all about the philosophy of unionism which has been woefully neglected in popular understandings of the civil war/why people fought. I would suggest you go read Gary Gallagher's (uva historian) books to get a fuller understanding