Check Engine Lights

I recently purchased a '99 Sonata. It had a check engine light when I bought it (not sure for how long).
It was running pretty well when I first got it but now has developed massive
idling & transmission shifting problems. Idles very rough (dieseling fairly pronounced at ildi/low speed, 3-4k+ RPM for extended periods before shifting, at 55-65 MPH cruising speed if car does manage to shift there is a noticeable vibration from the engine unless it is allowed to downshift).
Ran diagnostics and got the following results:
P0171 - System Too Lean (Bank 1) P0125 - Clsd Loop Fuel Ctrl, Insufficient Coolant Temp P0303 - Cylinder 3 Misfire Detected P0705 - Trans Range Sensor Circuit Malfunction
Cleared the codes and drove until new check engine light came on:
Only P0171 - System Too Lean (Bank 1) returned.
Repeated clear and recheck same results.
So I gues my questions are:
What are the symptoms of a "Trans Range Sensor Circuit Malfunction" and could it been cuasing the problems I described?
Is it possible that the sensor (circuit) is the primary culprit despite the fact that the code hasn't returned on the diagnostic test?
Thanks in advance for your assistance.
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Sorry - BTW----
I have run some fuel injector cleaner through it (only 50 miles of driving since adding) and I have checked the EGR valve to make sure it wasn't stuck.
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I'm assuming you have the 2.4L 4cyl based on the fact you've checked the EGR valve.
P0125: You'll want to check your thermostat and coolant temperature sensor to be sure they're operating correctly. This code could be caused by low coolant, a stuck open (or partially open or incorrect) thermostat, or a malfunctioning coolant temperature sensor.
P0171: This means that the fuel management system needs to keep injecors open significantly longer than it expects for the oxygen sensor to read correctly. This could be caused by a vacuum leak, misreading air flow sensor, or most notably a misfire, among many other things. See the description of P0303 below.
P0303: Check your ignition components on cylinder #3. Check the plug for carbon tracks or wear. Replace the plugs as necessary. Inspect the wire for evidence of arcing. (I don't recall which two cylinders have coils on them, so there may be no wire to check.)
P0705: This is typically caused by a misadjusted trans range switch or an intermittently shorted or open switch. Replacing the switch on nearly every vehicle I've encountered has solved this issue.
It's probably in your interest to nose around the service information at www.hmaservice.com. There's a lot of info there which you may find helpful.
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