The ONLY reason the chck engine light ever comes on is because a sensor, somewhere at some time detected something out of the ordinary (so it could literally be just about anything). His symptoms are completely different from what Mopargal posted about her car. The fuel cap being loose or crooked can make the chck engine light come on in newer vehicles.
As far as the chirp and the traction control light:
1. When does the chirp happen? i.e. acceleration, cruising, any time regardless of speed and or acceleration?
2. Does the traction control light come on right after a chirp or do they come on at different times?
You can break the tires loose, iliciting a chirp from the tires, easily from 1st to 2nd and also without too much effort from 2nd to 3rd (I haven't tried it in any higher gears yet). I have also managed to get my TC light to come on briefly when "laying into it" from a standstill. Got a little tire spin and the light lit up at me for a few seconds and went back out.
Not sure when you're lights and sounds are happening, or for that matter how long you've driven a stick (any length of time and you'll know all that stuff anyways

). I could see though if someone were to regularly hammer down while accelerating that they migh experience many episodes of chirping tires and TC lights being lit up from aggressive driving habits.