Fan light and dash/gear selector lights

I have a 96 Ford Contour with 2 ongoing problems. 1st: car was overheating - replaced thermostat and water pump. Car no longer overheats but fan light is now permanently on. Fan is running. Tried disconnecting the battery but came back on and stayed on.
2nd: Dash lights - gear selector lights and heating panel lights are off. replaced fuse (several times) but keep blowing fuses.
Any ideas on how to fix these problems?

the fans have a dual phase resistor if it shorted that couold cause them to stay on also when you turn on def or a/c it turns the fan on if that switch is shorted it could cause it too.as far as the light it sounds like a shorted out wire could be a pain to find.