Your problem has nothing to do with Firefox. The problem is that you don't understand disk images. This is a problem that a lot of newbies have, so realize that you're not alone, and that this is a problem that really should be addressed by Apple at some point.
When you downloaded Firefox, what you downloaded was a disk image, in other words a file whose name ends in ".dmg". When you open this file, a virtual disk containing Firefox is mounted on your desktop. What you're supposed to do is copy the Firefox app from the mounted disk image to your Applications folder, but that's not what you did. You probably dragged Firefox straight from the disk image to your Dock. That is wrong. You need to first copy Firefox to your Applications folder, and then drag it into your Dock. That way, when you click the Firefox icon from the Dock, it will open the copy on your hard drive, instead of the one inside the disk image.
Once you have copied Firefox from the mounted disk image to your hard drive, you no longer need the disk image. Delete it if you feel like it.