Hello I will help you with your question,
This engine management system uses a Mass Air Flow sensor and does not employ a MAP sensor such as a Speed Density system uses so that is why you have not been able to find the sensor for this motor.
Let me know what I can do to help you with this
I think where they went wrong was they used a generic scanner to pull the codes. Sometimes these will misinterpert the manufacturers codes (P1XXX) Anything that starts with the P1 is not an OBD code so the translation may be off.
There are other years that a MAP sensor was used to sense EGR flow but this is not one of them. On the Hyundai accent of the same year there is a MAP/IAT mounted on the plenum on the 1.6L engine
I suspect that the timing belt/head replacement may be the root of your problem as there may be a vacuum leak or the timing may be off. I would have to start by blocking the purge line and the EGR and see if there is a change. Work/clean the IAC (Idle air control) and see if there is a change. The factory scantool will not provide much information so your best diagnostic will be to see what you can do to make the poor/surging idle change. These had a problem with the TPS and you did the accepted test, one more is to push on the front of the case to see if you can change the idle.
Let me know if you have the map as shown on the Hyundai engine and if the head was a 2003 head from a KIA.
I will do what I can to help you from here but this will be a matter of testing to find the cause and no silver bullet will find the problem. The timing can be checked by removing the upper timing cover, rotating the engine to the TDC mark on the balancer and checking the cam timing against the head.
This engine does not have an EGR valve that is external so you are left with the ISC or IAC. Here is a TSB about cleaning the ISC and throttle plates, the ISC is the other connector on the throttle body, you already know the TPS