What would cause the fans not to run on a 1997 century except when the air conditioner is on?
Fans are desigend to operated with A/C and/or defroster is on also when coolant temperature exceeds 235 degrees. Perhaps vehicle is not getting that hot or sensor located at the back side of radiator approx. 1/3 down from the top is defective
Why would a Ford Fairmont air conditioner only work for short distances before switching to heating in temperatures above 20C?
Possibly. A bad blower motor resistor would cause the blower motor to either not function or function only on one speed (usually high speed). The air conditioning system is probably set up such that if the blower isn't functioning at all, the air conditioner won't function. Otherwise the air conditioner would overheat.
What would cause a central air conditioner to make a dripping sound in the inside unit and leak water?
When air is cooled the water in it comes out (like mist forming on the outside of a class filled with cold coke) and this happens in the air conditioner. Normally the dripping water is drained way to the outside (or a drain) by a pipe. If the pipe gets blocked the water will overflow and the conditioner will leak water - get it serviced.