You absolutely cannot use a seperate FTP client with a NOF site without going through all your locally-published HTML pages and editing every single link!
NOF does not require you to publish locally before performing a remote publish either; I tend not to bother publishing locally, but send it straight to my test server space and examine it there in different browsers.
Just click on the Publish button along the top of the NOF window and work from there. It's very straightforward, so you can't really go wrong.
You can customise your server's folder structure from within NOF, but you don't need to for most sites. I only do so for one site - and that's because it has a large number of pages and I like to split them up into folders for each section.