There's a yellow light under my speedometer that turns on after I start my engine and turn on the headlights. I randomly see my car with its headlights on the day after parking it and making sure I turned them off. I'm afraid my chrysler sebring's battery will die overnight due to the random times the headlights are on. The symbol looks similar to parenthesis with an exclamation point in the middle (not exact description).

Your battery is not charged and gets drained constantly, dome lights doesn't take much voltage to be lit. Get a voltmeter and check on the battery. Engine off it should be all charged up and 12V ish. Try to start your engine, should be 13-14v charging, if not, then it is your alternator not charging or SOMEHOW your battery doesn't receive enough charging from the alternator.
When you turn on the headlight while engine is running and died off because the alternator some how couldn't supply enough current to power both headlights and motor ignition system
Get your alternator tested, before that all connections between alternator and battery is NOT LOOSE, or broken or damaged. Then go to auto electrician. Then sort out your fuses later.

Check out all your fuses inside cab and under the hood

did you manage to fix this problem as i'm having the same problems. the car had a flat battery so tried jump starting it but no luck, replaced battery but can only get headlights/windscreen wipers/passenger window and hazards to work. car won't start and alot of the interior controls are dead, i've checked fuses (replaced 2)

I have the same problem, It seem to be a relay that doesn't engage making a clicking sound under the fuse panel near the steering wheel happens most of the time when it is hot. playing with the ignition key a few time do the trick for me. wish I had a better explanation/solution for you and myself though.

Sounds like an alternator problem. Check belt to make sure it's tight, then have alternator tested.

check alternator fuse!! if its blown....

under the intake manifold at the rear of the engine there is a pack of wires. This pack rubs on the bottom of the intake and creates a short circuit which screws up the !!speedo!!, sets off the check engine light and gives a trouble code (if you know how to read the check engine flashes) that there is a problem with the O2 sensor, and sometimes the headlights would surge.

Just crawl under the car when it is up on stands and gently turn over the pack of wires under the intake to expose the bare wire or wires. Tape them up and away you go.

Not sure exactly where the problem is but I can tell you that you have a bad ground somewhere. Check the ground circuits to the Instrument cluster.

change the part that its not comfortable in yore buzzer

there are more wires that you cannot see that are melted that is causing the problem. trace all of your wires, starting with the license plate light, all the way to the headlights

It needs a new headlight(or multifunction) switch, or you can just not use the automatic setting.