If you don't have the manuals, here are two links: SF series install
and Parts manual
they might help.
You mentioned that the unit worked correctly only one night. Were you operating on battery or 120v when the problem occured? It will be normal to have hot air flow out the furnace exhaust and it will be separate from the interior airflow which is generated by the fan's rpm and the temps on the inside wouldn't be as hot as the outside exhaust because of the heat loss of the ductwork and airflow.
Your question, what is 12v supply, it is the 12v supplied by the battery or the converter when connected to 120v. If you do not have the correct voltage because of a weak battery or converter, the furnance will not operate correctly.
All things being equal, might check the duct work at the casing and make sure they are connected. Your thermostat, mounted on the wall, is basicly a switch that tell the heater when to come on. If you can raise the demand for heat and the unit comes on, lower the arm and it goes off, I would guess the T-stat is operating correcly.
Hope somthing helped.