1.) If I dump a site, then click on the downloaded site. I am able to hit the locally cached version. However, if I close the application - the site needs to be downloaded again. Why?
Not sure I understand, Web Dumper doesn't use any cache. It downloads files and save them to your hard drive.
2.) The dumped website in their respective folders are empty. Why?
Open the preferences and click on the factory default button. Then try again.
I purchased this application on a whim based upon my understanding that I an download sites, and browse them off line. Is this incorrect?
Yes, that's correct.