My best guess, based on what you have mentioned, is that your unit is low on freon. Your emergency heat is always on, which is indicative of the compressor not running, especially in your relatively warm nighttime temperature.
The only thing not fitting this scenario is that usually the outside fan does not run when the compressor isnít, but at any rate whatever the problem is, you need to get a professional in to analyze the unit.
Sometimes, it can be a miss-match between the thermostat, inside, and outside units, but thatís not always a problem.
If you donít like what you hear from one guy, seek out an estimate from another.