2000 Chevy Malibu fuel/start up

I have been having problems since mid winter with my car starting. When it is below freezing it never wants to start especially if the fuel is half or below. Ususally it starts when the tank is full and its warmer outside or the engine is warm. Lately this has not been the case, it turns and sputters but won't catch. The gas filter has been changed twice in the last 5-6 months, thermostat is good. My theft system light comes on every now and then I heard that can be an indicator that something is wrong with the computer? Also my check engine light has been on since the last time the filter was changed. I make sure to change the oil just before 3,000 miles which is about every 2-3 months and never go to any nasty gas stations and try to take care of my vehicle. It's reallt starting to irritate me. My horn also doesn't work even with changing the relay, it occassionally overheats in the summer and I'm constantly adding coolant and my A/C doesn't work. My car needs to last another 6 months.