1. If the control is on Auto or any of the INT settings, it should be in Auto mode (the INT settings control the sensitivity). To test it, turn the key on, close the door, stand in front of the car, and splash water on the windshield. The sensor is up high, near the rear view mirror, so get the water up there.
If the wipers don't come on in that test, there's something malfunctioning. Try taking some Bon Ami cleanser and cleaning the glass over the sensor; if you have Rain-X (or similar) on your windshield, make sure you don't put it on the glass over the sensor, because those agents interfere with the sensors.
2.I've heard of people going almost 20 miles when it says 0 MTE without running out of gas, but the only time my LS said it had 0 MTE, I filled it up (I had just gotten back from a long road trip). It turns out that I had less than a half a gallon of gas left in the tank when it hit 0, which would be around 10 miles, give or take a few.