Idle s 2300rpm when cold, then revs between 1500-2000, while..

all fuel injected engine rev to around to 2000 rpm on start up then as the ECM completes its checks brings the engine back to set idle
run the fault codes as what you report may be a problem idle speed sensor (ISS)

Bleeding the fuel system is typically only needed on high pressure systems like GDI and Diesel vehicles, and only to get them to start if they run dry once.
If your engine keeps running but the idle speed moves up and down there are many things that can cause that. More information is always helpful. Does it always do it whenever the car is running? Or does it only do it conditionally (IE Only when 1st started in the morning, only after warmed up or getting off the dreeway, only with AC on or at night...describe as much as you can.)
Most newer cars have computer controlled idle strategy that wants to idle the car cold around 1000-1500 rpm (After an initial higher rev called a FLARE) and then bring it down in 3 or 4 minutes to 700ish rpm. If it CANNOT bring it down by normal means, then many resort to something called FUEL CUT IDLE where it actually turns off the fuel momentarily and the RPM will drop because the car is stalling and running out of gas...then back on and it starts to rev back up and when it gets too hiugh it turns back off. Cars that do this can have annoying surges from 500-2000 back and forth at idle forever.

a vacuum leak or MAF meter problem can cause rough idle. ALmost any engine code that turns on CHECK ENGINE lamp may be suspect, does it have any current fault codes?

As well, consider Sticking manifold runners, EGR systems, and temperature sensors all can cause surging, so can a defective Oxygen sensor, slightly jumped timing, and dirty throttle plates the ECM wants to close more but they wont due to dirt. If its not something fairly obvious, it may require deeper checking.

Your toyota technician should know what a "cold starting solenoid" is. It is the little thing that works your throttle until the motor warms up and something else takes over. I'd suggest going to another technician.

try to disconnect the master air flow sensor ( maf ) and start the car and see if there is any change on your idle if there is any change you found your problem

Is the radiator fan running when the ac is on ?

check the MAP sensor (manifold absolute pressure). The ECM (car computer) uses that to keep idle at minimum 750 RPM. It's normal for it to run high when cold. These small 4 banger motors typically run hot, and they won't run right IF they're NOT running hot, ergo the idle is usually high when it is cold so as to cause it to warm up quicker. If the RPM's drop below 750, suspect the MAP sensor, &/or ECM.

Okay, when this car is cold it idles at a higher rpm which is normal and may even lower the rpm after a few seconds, this is computer controlled and normal.the problem you list is that after it reaches operating temp the idle is up and down and even stalls when at low idle.There are few things to check, you have replaced the plugs and fuel system flush and temp sensor replaced. the next thing to do is to take a look at the throttle body, remove the air intake hose coming from air box to engine. clean the throttle plate, this is the plate that opens as you step on the gas pedal. I have seen dirt (carbon) build up on edges of plate and around the housing, this will restrict air flow at closed throttle and will cause the condition you are having.The next thing is to make sure there are no vacuum leaks, check around for hoses broken or split, spray around intake and throttle body with some carb cleaner and see if engine speed changes, if it does then leak is at area you are spraying.
Have you had the computer scanned for codes? these codes if any would help in finding the problem.Also make sure the air intake hose from air box is not split or has any cracks.the other problems i have seen is bad o2 sensor cause this condition, a scan tool would be very helpful at this point , you would be able to watch the sensor reading to see what is going on when the idle is acting up.Not sure if the ignition system on this car is sparkplug wires or coil over plug but i would also make sure which ever one you have is good, this is why scanning for codes is the first step, go to an auto zone and have them check the computer for codes, they do not charge. if there are codes write me back and let me know the codes. good day.

Have your alternator checked at your local alternator/battery store.. it sounds like a diode has gone bad...

it will idle high with air con on and revs will go up and down try turning air con off it that fixes it then there is no problem

try coolant temperature sensor