I know analog guys don't like to hear this, but a small microcontroller could easily meet all of your requirements. It would be easy to modify its operational parameters even after the hardware is built, and it would have by far the lowest overall parts count.
A built-in ADC could digitize the audio (as well as the voltages from your control knobs), individual outputs could drive the LEDs, and a single PWM output could drive your motor (with suitable output buffers, of course).
Yes, that is correct. Usually a single supply op-amp will saturate quite near the negative rail. If the negative rail is ground, then it cannot output a voltage less than ground by itself.
Not all op-amps are suitable for use as comparators. Some, for example, effectively have diodes between the inputs. Recovery from saturation may also be rather slow.
Best Answer
At the top of the chart it says "Vcc +- 15V."
Then it gives the maximum output values Vom as +- 13.5V. So, it does not have rail to rail output.
Then look at Vicr. That's common mode input voltage range. Typical is +-11V when operated on +-15V. So, input is not rail to rail.