Let's see if I can answer some of your questions...
1. The input stage: Some likely needs for bandpass here are reducing RF interference and AC coupling the input in case the source happens to have any DC offset. Rolling off some bass and high-freq outside the frequency range of guitar is also very usable.
2. I suppose the value was chosen mainly to suppress oscillations. Lower corner frequency undoubtedly works as well.
3. Yes, the switches are on at the same time. It's a dual switch.
4. In non-inverting opamp configuration the DC offset is lowest when DC resistance from non-inverting input to ground equals the resistance of feedback resistor (R12=R13). However, without the capacitor there is an alternative DC path to ground through the tone control circuit. This is in parallel with R12 and since the tone control circuit's impedance is rather low it imposes a considerable effect. A capacitor can break this path. If you wish to get rid of the output cap then adding this coupling cap may become a considerable tweak.
The unity gain issue and C3 & R5. No, this can't be modified but you can add a 100K series resistor to VR1, which limits the gain drop to unity when VR1 is turned to zero ohms. However, unlike the drive channel (which already has this limiter) the clean channel has no individual volume control. I suppose you could (similarly to drive channel's arangement) add one to "upper" signal path that goes to SW1b.
Unfortunately I can't take credit for the idea of different color LEDs. It' just the inherent nature of the dual LED package or "bi-color LED". The following is a direct quote from wikipedia:
"Bicolor LED units contain two diodes, one in each direction (that is, two diodes in inverse parallel) and each a different color (typically red and green), allowing two-color operation or a range of apparent colors to be created by altering the percentage of time the voltage is in each polarity."
It is a pretty nice invention because a digital control signal (either 0V or 5V) can easily control the color of a "single" LED (see attachment). Nice way to tell when things work (green) and when they don't (red) using a single indicator. The schematic displays the component a bit strangely (it should have three pins) but anyway, I suppose you got the idea.