There are probably module diagnostic codes an everyday OBD reader can't see that may be helpful to troubleshoot. A standard OBD reader basically reads check engine codes.
P0456 is a small emissions leak, perhaps because the fuel door is not sealing completely. Should not be affecting starting and running.
For P0205 and P0206, The Powertrain Control Module (PCM) monitors the continuity of the injector circuits as well as the voltage spike created by the collapse of the magnetic field in the injector coil. Any condition that reduces the maximum current flow or the magnitude of the voltage spike can cause this DTC to set. Given two cylinders, you may have a poor connection to injector 5 and 6. So check for cable harness damage or connector corrosion. Did you see any corrosion in the PCM connector when you replaced it, or wire damage? Anyway that could be an intermittent issue.
As far as shifting, are you sure you didn't accidentally bump the shift lever or paddle shifters? Are you saying the Jeep also stalled? If so did the dash light up like a Christmas tree? The transmission gear selection is controlled by the PCM, which you replaced. Not sure off hand what would cause a spontaneous downshift or shift to neutral/park unless the shifter is being flakey and sending neutral/park commands. The too fast to shift notice is just a side effect, probably because you were moving too fast to downshift to the next gear or to engage park.
As far as the service electronic brake system, we need the ABS codes for that. It could be as simple as the brake pedal switch. Some OBD readers can read the ABS module.
With all that being said, sometimes low or marginal battery voltage can cause weird things to happen. So check battery and alternator cables for tightness and grounds for good connections. Monitor the voltage displayed in the vehicle info screen. Have the battery checked.
There is a haunted vehicle thread indexed in the maintenance/repair sticky thread that could have other possibilities.