Throttle plate spring is broken.
When engine is off throttle/gas pedal will feel fine
When engine is running, opening the throttle plate creates an air flow into the engine that keeps opening the plate wider and wider causing runaway RPM increase, the spring prevents this from happening.
Cold start/running issue could be a few things.
There are two engine temp sensors on all fuel injected engines.
One is for the dashboard gauge, it has 1 wire connected to it
The other one is the ECT sensor, it has 2 wires, this sensor tells the computer the engine is cold so the computer runs in "choke mode", rich mix high idle and advanced timing until ECT tells computer engine is warm.
If this sensor is telling computer engine is warm all the time then no OBD code would come up, and engine would run rough until it actually warmed up.
Easy sensor to test, never replace this sensor, test it
Read here for testing:
http://oldfuelinjection.com/?p=28