how to find the cap value? same old formula, shuffle the unknowns about .... 1/(2*pi*R*C) gives the frequency, so 1/(2*pi*f*R) gives the cap value for the -3dB point. supply voltage has no part in the formula.

So 47k and 33nF gives 102.6hz

47k and 100 gives 33.8hz

So when the frequency reaches the cutoff you get a -3db reduction? And whats the reasoning behind selecting the value/frequency? Does it matter which opamp is used?

That's right, except that the value of C6 is 33*p* not 33*n*. Which gives a way-higher 100KHz.

The general rule that I learned about designing op-amps was "don't amplify anything outside the bandwidth of interest". So if you're designing an audio amp, you don't want your amp to also amplify radio frequencies, or even ultrasonics. That's what that cap does - reduces the gain outside the bandwidth of interest. Personally, I think 33p is pretty small there, and I'd have used 100p (which brings the -3dB down to a still-not-audible 33KHz). But you could even stick 220p in and not really hurt anything.

In the same way that AC-coupling caps should roll-off unwanted mains hum at the bottom end (guitars don't play 50/60Hz notes - basses are a different story), you should have a scattering of caps in the circuit to limit ultrasonics and anything higher. You choose what you regard as the necessary top-end of audio. 15KHz, 18KHz, 20KHz, 22KHz, 25KHz are all figures I've seen given as guidelines at various times and in various situations.

Finally, no, it doesn't matter what op-amp is used. The op-amp's gain is so high the theory regards it as infinite. That's clearly an exaggeration, but the theory still works in practice. Any half-decent op-amp has *more than enough* gain for our sort of frequencies for the final circuit's behaviour to be determined entirely by the components we put around it, and not by the op-amp itself. You can design (for example) an inverting op-amp stage and try ten different op-amps in it, and it'll work exactly the same (same gain, same frequency response) with each one. The only time this starts to not be true is when you use either very old op-amps which were much more limited, or your design starts to push the op-amp towards its limits, or both.