Question edited for clarity, add maker and typo 'Alima'.
Question moved from AC Cars, maker of the AC Cobra.
Let's deal with the overheating engine first.
You may have air in the system
https://www.fixya.com/cars/r29872074-vehicle_cooling_system_no_heat
Or is may be the coolant temperature sensor not turning the radiator fan on, fan relay, or the fans themselves.
There are a number of things that could be the issue. Here is the fuse box diagram. You have two fuses and a relay covering the Air Conditioning.
https://fuse-box.info/nissan/nissan-altima-l31-2002-2006-fuses-and-relays
The system may need refrigerant gas, but check the fuses and relay first as it sounds electrical because the green signal light isn't on..
Much of the issues you have are ultimately controlled by the Body Control Module and you may have a computer communication issue. The only way to diagnose that is by an auto electrician with a pro grade scan tool computer to check modules, sensors and the computer networks. This is not a $125 scanner, they cost between $3.5k to $5k.