At minimum, for an Xbox-style controller, you should be seeing a vertical and horizontal axis for each of the two analog sticks, and an axis for each of the two analog triggers. From an original Xbox controller, you should also have six analog buttons (though they are usually treated as standard binary buttons).
Other than that, this looks pretty cool. Perhaps in a few years, we'll see stuff like this combined with WebGL to make an open-source, cross-platform gaming environment that goes way beyond the current crop of 2d Flash games.
I had a look at https://wiki.mozilla.org/JoystickAPI and it simply says "unsigned long axis: axis number being moved", without examplifying for a known device. Didn't continue digging to the actual implementation.
Left Stick X and Y, Right Stick X and Y, And another Axis used for the 2 triggers.
Yeah, I know how silly that sounds for the triggers, but that's how it works.
2) You can't actually use an xbox controller with a computer (and hence with firefox) anyway without a USB cable. You could use a 360 controller, but not the first Xbox.
USB xbox 360 controllers don't need any installation last I checked.