At the end of this long experience, I feel very satisfied because
I learned a lot about microcontrollers in general;
I learned a lot more about the Arduino ATMega328P;
I had some hands-on experience of Data Acquisition, not by using something already done but by making something;
I realized an amateur oscilloscope that is not that bad.
I hope that this guide will be useful to anybody that reads it. I wanted to write it so detailed because I learned all that in the hard way (surfing the internet, reading the datasheet and by a lot of trial and error) and I would like to spare anybody from that experience.