it's the wire harness that connects to either the crank position sensor or the cam position sensor. The plug end looks similar, and they are both right in that area, so I'm not sure which.
Yes, you have to get that connected for the ECU to control the engine properly. You probably have the pigtail that mates to that dangling off the sensor.
No, and wrong.
That is a 1 wire plug. It plugs into the back of the power steering pump, and controls the idle up circuit. If there is no sensor in the pump, it has either been changed, or the wiring harness/engine has been changed.