Low oil light on 2000 Ford Tarus stays on while ideling

The vehicle is nearly 16 years old now, so it is quite likely overdue for a major tune-up (including plugs, wires, and coil packs).
Beyond that, verify adequate pressure at the fuel rail, and replace the fuel pressure regulator and/or fuel pump as required. If fuel pressure is adequate at all load ranges, suspect fuel contamination (especially if you have been using ethanol blend fuels over the past few years). Replace all fuel in the vehicle with fresh in this case, and that should solve your problem.

The headlights are on separate circuits the only thing common to both sides is the on-off switch and the battery terminals

Adjust with switch on the dash in the location of the dimmer switch !Check it out on you tube !

You might check the pulleys that the serpentine belt runs on. Make sure all are free wheeling and not loose or rough or make noise. You would need to remove the belt to check them.

several reasons cause this problem the wire could be broken or the low oil sensor is defective or the engine is low of oil

You don't want to overfill your engine with oil. I'd recomend you change your oil and put the right amount in it, because chances are, if you are that low, it was time for an oil change anyway. As for your coolant leak, check your hoses and radiator, if you don't find anything look your engine block over for antifreeze residue. Usually when your water pump wears out and starts leaking it makes a big mess.

will it re-start right back up?
next time try to keep your foot on the gas pedal to see if it stay running ( be careful when you do this, if you give too much gas the car will over come the brake and cause accident )
if it stay running then you need to replace an idle air control valve

if the coolant is full you need to check and most likly change the low level sensor in the coolant tank.

This light will also illuminate if you have a hydraulic concern such as low brake fluid level in the master cylinder.