Difficult communication with processing

const int buttonPin1 = 1;
Pin 0 and 1 are already used by the USB<>Serial chip, so can't be used for buttons.

You can use the analogue inputs as digital inputs.
const int buttonPin1 = A0;

Example of a pin array.

const byte buttonPin[] = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}; // 14 is A0 on an Uno

A button can also be used between pin and ground, with internal pull up enabled (no external resistor).
Used in an array

for (byte i = 2; i < 15; i++) pinMode(buttonPin[i], INPUT_PULLUP);

Leo..