Looks like you got a PO411 and a PO412...BOTH are "cannot control RPM during engine run self test" 411 being low rpm check and 412 being high rpm check.
PO411....
Possible causes:
Improper idle air flow set.
Vacuum leaks.
Throttle linkage binding.
Throttle plates open.
Improper ignition timing.
Idle Air Control (IAC) solenoid contamination.
IAC circuit short to ground.
Damaged IAC solenoid.
If your car is idling normally....you've got a BAD Idle Control Valve.
PO412....
Possible causes:
Open or shorted circuit.
Throttle linkage binding.
Improper idle airflow set.
Idle Air Control (IAC) solenoid contamination.
Items external to Idle Air Control system that could affect engine rpm.
Damaged IAC solenoid.
Damaged Powertrain Control Module (PCM) .
It sounds like you've got a bad IAC valve for one.....
The EGR code I specified isn't a bad EGR valve, its the EGR pressure sensor thats located on the back of the drivers cylinder head.
There are two hoses that should be attached to it...take a small mirror and see if everything is hooked up properly. If it all looks ok, go purchace a new one.
If you're going to attempt to tackle the IAC valve...I HIGHLY recommend you replace the TPS sensor at the same time, I'm thinking this might also be bad giving you the transmission symptoms.
So....you need.
Idle Air Control Valve and gasket
Throttle position Sensor
EGR Pressure sensor aka Differential Pressure Feedback EGR (DPFE)
And if you can get the right one, replace the throttle body gasket.
Now....as far as the check engine light being OFF....on OBDI cars, the light won't come on unless its a "hard" failure, but it will store any "failures" into its memory as a "history code". If the same part fails 3 times, than your light will come on. Thats why you haven't seen the light....but that doesn't mean you don't have failure codes.