Okay. You have multiple problems.
In the headlight, check for toasted contacts in the plug that goes onto the bulb; chances are good that you need to replace that plug. If the plug's good, you may have a bad wire in the wiring harness, but my money's on the plug.
The air compressor's probably running continuously because the air shocks, the air lines, or the connections to the shocks are leaking; the only fix for that is to find the leak, and replace the leaking components. Be aware that aftermarket air shocks are smaller, and WILL NOT achieve the same amount of ride height control as the factory units.
Like any GM car, the usual things that cause the power door locks to fail are faulty switches in the driver's door, and breaks in the wiring that goes into the door from the body. As for the automatic door on the passenger's side, I have yet to see one of these keep working well for more than 20,000 miles beyond the end of the warranty; unless you just like spending money, I'd write that thing off. Also, the contacts in the sliding door are temperamental; it's VERY common for them to fail to lock some of the time so that the door's not locked, but the alarm is set - and it goes off when your kid runs out and yanks the handle. Likewise, one or both of the sliding doors often don't unlock. Sometimes, it improves with cleaning the spring-loaded contacts in the front of the door with some electronic contact cleaner spray - but it usually goes right back to misbehaving after a short while, and some of the sprays will attack the paint and/or plastic, so you risk making the situation worse by using them.
Last but not least, a remote that's still working on a car that's 11 years old is unusual, but you can try replacing the battery and carefully cleaning the switch contacts inside the remote; crud builds up on them and makes them stop working, and *sometimes* a little cleaning is all it takes.
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