My turn
E=IR
First: it's a DC circuit, so there is no impedance in the circuit due to a lack of frequency (other than zero hz). There is only resistance. If one were to consider the initial near-instantaneous charging time of the circut, then there is a period of time which one could say there is a 'frequency' (due to the change in voltage over time), but this disappears once the voltage reaches full potential. Generally, in a simple circuit such as this (i.e. a non-radio high-frequency circuit), this initial time is not factored into the design, therefore no impedance.
Second: I understand these circuits to be current-controlled or current-sensing, not voltage-controlled (the voltage doesn't change in the circuit, the current does - this is how it knows when the plug is hot enough). If one changes the glow plugs for the wrong voltage, generally the resistance of the plug is not correct, so the current flowing through it is either too low (glow plugs stay on, the circuit only shuts off when it times out) or the current is too high (glow plugs heat up quickly and the circuit shuts off, usually too quick to hear the second click, so you think it's not come on at all). This is a similar problem to when a turn signal bulb burns out and the signal flasher clicks faster (the current draw goes down, so the relay 'clicks' faster to tell you a bulb is out) - same thing happens when you change the bulbs to LEDs (they don't draw enough current, so the flasher relay thinks there's a bulb out and flashes faster).
If you have a bad plug, resistance of the system is off, which means the current will be wrong, which means the circuit won't cycle properly. Because the four glow plugs are ganged together with the bus bar, one bad plug messes with the whole circuit.
The temperature sensor is used to tell the ECU if the engine is warm enough to not require a glow plug cycle. This component doesn't sound like it's a part of your problem.
NOTE: I think I've got my inversly-proportional resistance effects right-way-around, but if not I apologise - I pulled this all off the top of my head and I'm answering submarine questions at the same time so I'm a little distracted (with this).