When a webserver serves out a volume directory, it usually has an index of the directory or can create one on the fly to display the contents of the folder to the www. That appears to be what you are seeing. file:/// is the url for a directory location, just like http:// is the url for a web location. Safari passes those urls off to the Finder for display, and apparently, Firefox will create the index.html file and display that (even though it is a browser and not a server).
I think that covers 1 to 3. As to 4, I don't know. Maybe you accidentally dropped something from the Applications folder onto the Firefox browser and it indexed the whole directory. I don't use Firefox, so I'd just be guessing.