That shiny cylinder is held in up position by a spring. This is a position when the valve is open (full flow and heat). When electric current is applied the cylinder will be pushed down against the spring, closing the valve (no flow, no heat).

1. When the spring is corroded the valve will be closed at all times at idle or low RPM. At higher RPM the valve will open by the pressure of water. In other words you will have cold, heat only when keeping RPM high.

2. When the coil is bad the valve will be open at all times. This means full heat at all times.

3. When the rubber is broken water will enter the cylinder area. The seal doesn't appear to be absolutely tight, I think there can be some limited water in the cylinder area without affecting its operation. In that case you will have the valve operating sometimes and sometimes not.

The climate system is designed in such a way that should the controlling unit be faulty you still should be able to turn the heat completely on by rotating the wheel to the hottest position or completely off. No modulating of temp takes place. In your case, when you are able to turn the heat completely off (or completely on) but nothing in between I am afraid the valve is OK and the fault is with the controlling unit itself or the thermistor that tells the unit what temp your environment inside is.