Ok, I mis-read the numbers in your post. I now get it. My answer stands, though; "Get Info" doesn't include files you don't have permission to read in the count. 7GB is small enough (relatively) that it could just be system files; sounds a little big, but not ridiculous.
And in answer to the second question, sparsebundle disk images are (basically) disk images that can expand the actual size on disk as needed, when you add things to them. Spotlight uses them for network backups, for example.
The issue described is when you remove files from a Sparsebundle but it doesn't get any smaller on disk. I admittedly don't have much experience with this, but I believe that this space would be visible with a "Get Info", it just shouldn't be being used.
As for identifying the source of your "missing" space, there are programs that will visualize it for you, though I can't name any off the top of my head--a VersionTracker search might help, or maybe someone will recommend one. With 7GB, though, it's probably nothing out of the ordinary, though there's some chance it's a "stuck" cache file or somesuch.