If you look for the model number you can get the manual from the manufacturer or the document center here.
Now to answer some of your questions.
The runs on 12 Volt DC from the battery
or the converter. It will come on when the thermostat is adjusted to a point where heat is called for. When heat is called for you should not be able to read any voltage across the two leads coming to the thermostat. The thermostat is simply a switch, you can take a jumper and connect the two leads together and the fan should come on.
The fan has to be running and move enough air to move the sail enough to allow gas to flow to burner. Without enough air no gas no flame.
Once gas is going to the burner the igniter sparks and you get flames. When the temperature at the thermostat reaches the temperature the thermostat is set for the switch opens and gas stops flowing. The fan continues to run for 2 or 3 minutes then shuts off.
I have has the one small wire inside the thermostat brake in such a manner you couldn't see that it was broken. A new thermostat was less than $5.00.