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Thanks for reaching out.
That's a nice project, if you want to use an ADC I recommend you to check the Schematics for the Intel® Edison Board for Arduino, to see how the ADC is connected to the Edison using the SPI interface.
Commonly for the microphones, it is recommended to use a signal conditioning circuit and I think there are too many configurations for it, but you can check these links for general circuits:
About the speaker, I think you should use the PWM outputs for it, there is a lot of information about it too that you can search, like this link: https://developer.mbed.org/users/4180_1/notebook/using-a-speaker-for-audio-output/
I hope you find this information helpful.