I can't explain all the wavy hands and proximity stuff you are seeing. I have used that same sensor and it just worked as expected.
Perhaps you should add a bypass filter capacitor of .1ufd (or larger) between the hall effects Vcc pin and ground pin. I don't see anything wrong with your sketch.
Edit: You might try using a diffenet output pin for the led and change your code to match as maybe you damaged the pin 13.
Lefty