Hello, Pizza Guy is the best no question on that front but I will try to help with the AC system issue.
1) Is the a/c compressor clutch engaging?
2) If not check that fuse as well.
2) If it is engaging are the lines getting cold to the touch?
3) I looked at the schematic for the FCM question. I did see where the FCM gives a signal to the PCM. PG 546 or 7-2.Then the PCM communicates with the ECU and AHCM. You can download the service manual( available on this forum) PG.4130 or 24-1 starts the A/C troubleshooting information and the schematic can be found on PG. 4189 or 24-60.
If it makes you feel better within three months I had a top hydraulic cylinder go bad, CSP/SSM module/wiring harness, alternator,A/C controller, TMPS sensors replaced, and I just repaired the valve cover breather due to it leaking oil. This is all in a very well cared for garage kept 05 SRT with 91,000.
These cars are starting to get some years on them and it takes a devoted person to keep them up and running.
I hope I helped.