Electronic – input stage (pre opamp) for voltages between 0 and 240V AC

Generally a guitar amp would have about 100k (or greater) input impedance - this is because the tone controls and volume controls are about that sort of range. Yours has 10k input impedance. I'd make R8 100kohm and R7 1Mohm

Your 2nd stage is not needed - it has unity gain for the relevant frequencies and your filter cap might just as easily be placed across R7 but obviously 100x lower in value because R7 is 100x bigger than R10. But having said R7 needs to be 1Mohm (above) the cap needs to be 1000x lower like 15pF.

I'd also use an input jack socket with an earth switch integral then you can disconnect the battery when not plugged in.

Yes, the output power is almost always greater than the input power in op amps. Ideally, the input power is zero since the input resistances are infinite.

Here's a pinout for an 8-pin 741 op amp:

See the pins labeled +V and -V? Those are for power supply voltages. That's where the output power comes from. Conservation of energy is not violated.

Here's a non-inverting amplifier circuit that illustrates this. I included a bias current between +V and -V of 2.8 mA, which I took from a datasheet. As you can see, all power is accounted for. Surprisingly, only about 1/6 of the total battery power is delivered to the load! This is due to the large supply voltages and the low output voltage. You'll see this same low efficiency for the same reason in linear voltage regulators such as the 7805 and the 317.

^{simulate this circuit – Schematic created using CircuitLab}

Warning: CircuitLab does not simulate op amp supply voltage pins correctly. If you try to simulate this circuit, you will get no current on +V and -V.