Is an analog stick considered as a button? Because there could be 2 buttons and a stick.

i would consider 1 axis as 1 input, so 1 analog-stick is 2 inputs. (x- AND y-axis)

But thats just my opinion...

you will have ask the judges on this but a button is something you push and is on or off.

An analog is not a button (unless your pushing em in for the toggle). The  D pads are buttons, and if you use the arrow keys they are buttons. So you are quite limited I.e. only up and down or only left and right ect.

Tough, I'm not aiming for this, i need control and fire.

Thanks a lot!

When I first saw the wildcard, I though of a game that only works with two gamepad buttons, like a chrome dino-like game with the xbox A button to jump and the xbox B button to crouch.

About if you make your game playable with only one button 

The wildcard isn't considered in the judging, just think of it as an optional challenge for fun. My take on it is that you interpret it as you like :)