If you're bandpass filtering and then peak detecting, your output is going to be essentially a DC voltage corresponding to the strength of the received signal. Well, it may look more like a sawtooth wave with a DC offset, depending on the time constant of your peak detector.
duty cycle determines the brightness of the LED. Obviously, a 100% duty cycle would make the LED be constantly on (bright as possible), and 0% would make it be completely off. However, here you need your signal to be modulated at 20KHz so you can't run it at either extreme. 50% duty should put the most energy into the 20Khz frequency component, which is what you want... any energy you waste in the harmonics won't contribute any performance to your sensor system.