I can see a couple possibilities. The first is that your heating sensor is bad. You have two sensors on the plastic pipe coming out from the front of your engine. One could be bad, I don't remember which goes to the temp gage and which goes to the alarm, but that's a place to start. Does your temp gage show high temp or is it just an alarm? If it's just an alarm, unplug one sensor and see if the temp gage drops to zero. If it does, then the other one is for the alarm.
The second possibility is that that circuits on the back of your dash are flaking out. Your instrument panel may need to be replaced. This could explain the dash lights as well.
Have you checked the bulbs on your dash. Have you checked the light switch. Remove the switch and test the contacts for the dimmer control with a multimeter. The resistance should change when you rotate the control in opposite directions.