Yes - when I turn on the Diesel Burner switch (its associated green light comes on) I can hear the burner first turn on and a few seconds later I can hear the ignition and initial combustion followed in a few more seconds by a short burst of black smoke coming out its exhaust pipe.
Yes -  when I turn on the Engine Preheat switch (its associated green light comes on) I can hear the engine preheat pump start humming.  Well before starting the Engine Preheat the AquaHot should have been heating by either the electric water heating element and/or the diesel burner.  Both the electric element and Diesel Burner can be on at the same time.
On our AquaHot, the AHE-100-02S model, there is no control panel remoted from the Aquahot unit.  Its brains are all located on the front wall within the unit's stainless steel box beside several auto-fuses and four thermostats.  If the unit faults, then we simply turn off the diesel burner switch and turn it back on to reset it.  If it doesn't reset, then I start looking at the fuses.