Ok, if your temp guage is swinging to red immediately when cold, that's going to be your temp sensor. They do go bad from time to time.
When your standing in front of the car, looking at the motor, you'll see the air inlet pipes leading into the throttle body, on the front of the intake manifold. Look down past the throttle body to the right, you'll see the sensor mounted on top of the water pump.
That's the bad sensor.
As for the coolant warning, was the coolant low? If it wasn't, you've got a bad level sensor as well, and they also go bad. In this case, the level sensor is mounted in the expansion tank/ coolant reservoir assembly, mounted in the fan shroud on the left of the radiator.
As for the coolant itself, when you fill the radiator, there's a plastic bleed screw that looks like a phillips screw, next to the radiator cap.
Unscrew the bleed screw, and fill the coolant reservoir slowly. If the system is empty, you'll be able to pour two gallons into the radiator, maybe a little more. Replace the bleed screw and start the car, with the radiator cap off. Rev the motor slightly 3 or 4 times, and recheck the coolant level- top up the reservoir until the red 'level rod' in the center of the reservoir is a little bit above the neck of the expansion tank. Put the cap on and you're done.
Bleeding the system is important, so take your time with this. Also, after the car cools down again, you can re-bleed the system if you'd like the extra peace of mind.
Good luck with this!
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