solder not sticking/board question
The brown stuff you're seeing on the right side is the bare circuit board -- the copper has been completely torn (or burnt) away from that pad.

There is, generally speaking, no way to repair pads that have been destroyed to this degree. Typically, you will need to find another point on the board that's part of the same circuit net and run a wire to it.

In this case, however, I suspect that the missing pad is not part of the circuit at all -- that pad looks like it is simply used as a mechanical "anchor" for the joystick. If this is the case, you may be able to leave that pin unconnected, or use a standard adhesive (like epoxy) to help hold the joystick in place.

To avoid this problem in the future, turn down the temperature on your soldering iron. Don't set it any higher than needed to melt your solder.