Issue has been covered before.
Do a forum search.
Does the ceiling lamp illuminate when the driver's door is opened? If no, the most likely culprit for the key and headlight warnings being inoperative is that the driver's door jamb switch has been knocked apart (usually by closing the door with the seat belt buckle hanging in the door opening).
Simple fix if that's your problem - remove the switch and snap the pieces back together. Rarely will you find a switch that is so damaged as to require replacement...
While I do agree that the key and headlight reminder can be tied into the door switch (they only activate when the multiplex sees the door open with the headlights on or the key in), I disagree with the damaged switch comment and following this advice would have customers at my work coming back with repeat complaints and not having their vehicle fixed right the first time.
Every single door switch of the pin-design I have replaced at work has been damaged in some way. The little loop tabs that hold the switch body to the mounting plate have broken on either one or both sides, or the pin assembly body has cracked and broken away completely. If the door switch has come away from the mounting plate and it is your own vehicle, then yes you can try to put it back together or crazy Glue it and see if it holds, but don't be surprised if it comes away again in the near future. Besides, for the price of a door switch it's an inexpensive repair when you figure you'll probably only replace one or two in the grand scheme of things, either of which can be done yourself with nothing more than a ratchet and an 8mm socket.
The headlight-on warning being out implies that the buzzer itself is bad. IIRC that function is unrelated to the door switch or the seat belt switch.
You could make a point of turning off your headlights, and rejoice in the lack of an annoying buzzer.
I could be wrong Dan but I think the door switch does have a say in when the reminders are activated.
The MICU watches it's inputs of which the door switches are one of them that tell the MICU when a door is opened. So if the MICU sees the door open signal but also sees the key-in signal and/or the headlights-on signal then it will sound the appropriate reminder (I believe the key-in reminder always takes precedent over headlights on, thus key-in reminder will activate but headlight on reminder will not until the keys are removed). So if the door switch is broken and the doesn't ground and complete the circuit when a door is opened, the MICU assumes that the door is closed and won't sound the appropriate reminder when the key is left in or the headlights are left on.
However, the fact that the MICU doesn't rely on the door switch to determine when to sound the seat belt reminder does make you wonder if it has been disabled as Mook said or if the buzzer is bad as you mentioned.
I could be wrong but I think the buzzer is located in the MICU (I had a multiplex out of a Pilot which was bad and there was a buzzer assembly in it (looks like a little capacitor with a hole in the top) so if you could find someone with the same Element, it would be a matter of changing it out for a known good unit and see if the problem remains.
