Elements may have more than one class. The class or classes that an element has are usually only for styling. The demo page was meant to convey that you could also have other classes for styling (really for whatever other) purposes you might need or want them for. All that's required for the link to be a toc though is that it have the toc class and be in the paginate division for that slider.
As to your other question, that looks like ordinary HTML/css. If so, it will behave the same way. Background or any other images must be on the server to work live. Except if you test your page live and it references images on your hard drive, well they are still on your hard drive, so they may show up for you, just not for anyone else.
If you want more help:
Please post a link to a page on your site that contains the problematic code so we can check it out.
Bookmarks