Hello, as far as the air conditioning system goes:
Air conditioning problems can originate by one of the following general areas:
1) A problem with the refrigerant system. Meaning, the refrigerant used has escaped and there is not sufficient refrigerant to pressurize the system properly, resulting in hot air. When this happens, the system must be checked for leaks, the leaks repaired, and the system recharged.
2) A problem mechanically or electrically with the under hood components. If the compressor has failed, it will not allow the system to operate. Further, if the system becomes contaminated with debris from a failed compressor, this can be even worse. Electrically, the coil of the compressor may not be working properly, or a cycle switch could fail preventing the system from operating. If your condenser fan is not working, the system may not work properly also.
3) Climate control problem inside the vehicle. If the system that operates the heating, ventilation and air conditioning system fails to operate properly, then the under hood components may not be turned on or off properly, keeping the cold air from being produced.
Only testing these systems will yield a direction and an eventual result.
Regarding the hesitation -- this can be related, but may not be also. Treat the concerns separately, but approach the air conditioning system concerns first.
