6. Will the circuit work as a whole?
You will get severe volume interactions between the two channels when you adjust their individual pots. For instance if adc_out is not required to me in the mix then you would adjust RV1 to ground the wiper but, unfortunately, this will also ground the wanted mixed_mono signal. Result: total interaction and not really a mixer.
3. Will setting RV1 or RV2 to zero cause a "jump" in the volume of the other source? If yes, can i put a small resistor in series with the pots in order to avoid this effect? How small?
It may need to be as high as 100 kΩ to overcome the problem and, you might start to hear a little resistor noise.
1. Is the stereo-to-mono "circuit" correct?
Yes, that will suffice.
Are the values of R8, R9, RV2 ok?
They are OK.
Is R27 needed?
If you didn't have it then when RV1 volume was turned fully up it would kill-off the mixed_mono signal.
I strongly suggest that you to use a proper mixer circuit using an inverting op-amp and forget this cranky method.
8. Can R25 be safely removed?
9. Is 470k a sensible value for R28?
10. I am powering the opamp with a single 5V supply, is it correct to ground the positive input or do I have to bias it at 2.5V?
Yes to questions 8, 9 and 9 but, for question 10, you need a dual rail supply for the op-amp or, use a 2.5 volt bias and add coupling capacitors connected in series with the potentiometer wipers.