You are asking me to give you 25 years or experience and training in a text forum. There is now possible way for anyone to say what is exactly wrong without looking at a data scan tool that has designed software for your car to really offer a silver bullet repair.
" 7500 rpm then down to 5000 and finally back to 7500 were it should be. It has already done 1 were the engine was really pulsing before the IAC "
I hope you mean 750 hundred and not 7500 thousand rpms?
The problem with a IAC is there is no feed back to the ECM for diagnosis. It is a dual DC motor driven in both directions by changing the power -+ several times a second. The controller only knows the wire is intact. It has no way of knowing if it actually moved.
The ECM will figure out that the rpm is to high by watching the TPS and crank signal and others small inputs. If the IAC is not able to bring the idle up or down The ecm will attempt to control timing and pulse width of the injectors for idle control. slow at doing this.
The problem is that Technicians are telling all is ok when they are not really sure what is what they are seeing on the scan tool. The controller will not lie.
In the above post I asked you to give me the long term and short term fuel memory and tps, iac. I can tell you what the controller is trying to do.
I get 400.00 for starters when people bring me their cars for this type of issue. Its not easy and it takes time.