I'm no expert and i'm no electrician, but i've tinkered guitar amplifiers several times and made some effects pedals...
Those JRC4558's.... they're legendary chips in their own right - they give a very warm noise close to that of valve amplifiers. I don't think the audio properties looked that good for them on paper, but something about them made them sound amazing. The first section of your circuit, leading up to the master volume control has a gain of 0 - i think it's there solely to give this warmer tone to the audio. It might be noisy or sounds poor, but it'll give it an amazing warm tone - sadly you might need to be a guitarist to notice it (I haven't had the honor of hearing one
My theory on C13... Pots tend to wear away fairly quickly as they get swiveled, to the point where the metal tracks start to wear away and you get places where you lose contact. This gives a horrible clicking/clacking noise when you pass over them. I'd say C13 is there to lessen the effect.