Whatever that bar is, it's not Mozilla official. Some other software on your computer put it there.
Why does Firefox allow this?
We can't prevent this from happening so we try to provide a good way for other software to do it, so they don't do it in terrible ways:
http://code.google.com/chrome/extensions/external_extensions...
This is a historical accident; only toy and mobile OSes have any sort of application-level access control.
Wrong, they can just add DRM.