Body Control Module and Powertrain Control Module ?
 

I own a 2013 Camaro ZL1 Convertible 6.2-liter V-8 6 speed & had it since 06/13. Ongoing problems with

1. Tire Pressure Monitor System
2. Check engine light - code P0300
3. Service Stabilitract

TPMS has been the main problem with the dashboard light going off then CEL & Service Stabilitrack, had the TPMS sensor replaced several times & reset but the problem continues. Dealer tells me they cannot find any problems with the CEL & Service Stabilitract & just reset it.
The car has been at the dealer multiple times ( 30 + days ) so I asked my regular mechanic and he said

"If he car is all stock then it more than likely needs the connectors at the BCM and PCM replaced. I have seen a ton of these have loose terminals inside of them that will cause this. In some cases I have seen the same connection issues at the fuse box under the hood but that is not as common."

Any ideas on what the problem could be and also what my mechanic mentioned ? Thanks in advance.