5.12. Why are both Up and Down treated as the same axis?

That's because they are the same axis. An "axis" on a joystick (or gamepad) isn't actually a direction, but a dimension. A standard simple joystick can move along two axes, the X-axis (side to side) and the Y-axis (up and down); when you move the stick to the left, you're moving it along the X-axis in the negative direction, and when you move it to the right you're moving it in the positive direction along the same axis.

What really matters is that in QJoyPad, every axis represents two opposing directions and can therefore have two different keys. I only do it that way because thats how the device itself works. I'd make the labels a little more intuitive, but unfortunately what each axis corresponds to changes from controller to controller and there's no way for me to know which is which. If you don't know which axis to set for which direction, move in the direction you want and see which button lights up, or try using Quick Set instead.