Your starting and idling problem sounds to be related to the IAC.
I see that you have a new one installed, so, assuming it is good, there are several additional items to check.
First, make sure it is plugged in! Then, inspect the "nostrils" in the intake to make sure they are not clogged. They are the upper pair of holes visible through the open throttle plate, the lower pair of holes is for the EGR. There is also a passagway through the throttle body itself for the IAC inlet air. Check it also.
For the 124 code, pull the TPS and make sure the center shaft connection is properly positioned on the plate shaft with a closed throttle plate. Some sensors can be installed out of phase.
If all of those check out, it will be time to get out a meter.
For the TPS, backprobe the center wire of the connector with the KOEO. It should measure just under 1.0 V (.6 to .95 V is typical). Monitor the voltage while opening the throttle by hand, the voltage should smoothly increase to around 4.5-5.0 V.
For the IAC, backprobe the RED wire with KOEO. It should read battery voltage. The other wire should have a variable voltage on it, depending on what the PCM is trying to tell it to do. If it reads the same as the RED wire while trying to start the engine, then there is either an open circuit in the wiring to the PCM or the output driver in the PCM for that solenoid has failed.
Hope this gives you a few things to check.
Steve
PS If you don't have one, Sears is currently selling a basic digitial meter (34-82082) on sale for only $9.99. If you wait until Saturday morning, you can save an additional 10%.