Having trouble understanding circuit diagram (paper touchpad)
The wires A0, A1, A2, A3 are they being connected to the Arduino?


Yes. I don't think it is explicitly documented, but read the code and it is a safe conclusion:

  //read the four corners
  a = analogRead(0);
  b = analogRead(1);
  c = analogRead(2);
  d = analogRead(3);



  The capacitors being used in the diagram, are they for stabilizing the signal?


Yes, that's one way of putting it. Consider the circuit without the capacitors, and it represents simple voltage dividers that will (probably radically) disturb the analog inputs for every miniscule change in the finger-graphite-paper connection. The capacitor/2MΩ combinations are RC circuits that resist sudden voltage changes e.g. if the finger has pulled the input to ground and then released, the capacitor essentially "discharges" via the 2MΩ resistor at a rate indicated by the RC time constant.