Furnaces starts on its own thermostat is off.

Sounds like the heat anticipator in your thermostat is either bad or out of adjustment. Turn of the furnace power. Remove the thermostat wires from the thermostat. Turn the power back on. Connect the white and red wires together. The furnace should start up. Let it run a couple of minutes. Then disconnect the wires. The burners should shut off immediately. The blower will continue to run for 60 to 360 seconds then shut off. If this happens replace your thermostat. If the burners continue to burn, then your problem is either the furnace or the thermostat wires.

You could wire the Humidifier to the HUM terminal on the Furnace integrated control board, this would allow the humidifier to start only when the blower motor energizes.

On properly sized furnaces there are a few controls to look at. Check the settings of the fan switch. If these are unchanged then there may be a reason the furnace is shutting off due to poor air flow and resulting high temperature. Check filter and verify air flow is good. It may be possible that a safety switch is failing and intermittently on and off. Are all the covers securely in place and hitting any safety switches? If not seated properly the cover may loosen when the fan runs and the switch shut off the unit. There is often a flame roll out switch that could have been strained. Lastly, has the thermostat been working long? Thermostats have internal heaters to stop the furnace which is called a heating anticipator. If the thermostat is near a heat source (heat duct, refrigerator, oven, person, hot water pipe), worn out, anticipator is set wrong (older electric thermostats have adjustable settings) or covered (yes, I have seen some covered) then the free room air cannot measure correctly and the thermostat cannot control what it cannot accurately measure. Of all these possibilities I would start with the thermostat and proper furnace air flow, second check the fan/high limit switch and third go component by component through the wiring diagram looking for defects in each component. If available follow the manufacturer's troubleshooting guide.

If the inducer runs for a short time and shuts off and the main blower comes on and runs it could be a high limit switch or a roll out switch.it could also be a pressure switch that is stuck in the closed position. Most new furnaces have to read the pressure switch in the open position and then the closed position after the inducer fan starts. . Hope this helps.

If this is a hot surface ignition system, the sensor may also be your igniter.

Make sure the kill switch on the blower door is closed, or furnace won't do anything. Then remove power from furnace for a few seconds, then try again. Still no go? Take a jumper wire and jump the "r" terminal to the "w" terminal on the furnace's board. This bypasses the thermostat. This is only for testing. If it still wont run, call service guy. Gas furnaces are not good things to tinker with.

The vent motor starts with a call for heat from the thermostat. They are actuated by a separate relay that may be arched closed. Kill all power, turn the stat way down and turn the power back on. If it starts when the thermostat is NOT calling for heat, find and replace the relay.

After you replaced the batteries, you also need to sync the remote with the receiver for it to work again. Here's the manual link: http://www.atwoodmobile.com/manuals/furnaces/MPD%2033179%20SP%201.08.pdf

Suspect that the igniter is causing the clicking (or could be a relay). Suggest having the furnace serviced. There is also a major recall for some models of the Coleman Evcon furnaces.

Could be a defective thermostat in the plenum.
When a gas furnace shuts down the fan(blower) will run until the plenum cools to the safe range. Usually 1 and 1/2 minutes.
Intermittent operation is a defective thermostat or relay.