The example uses the GPIO13 because it is the one attached to the on-board LED on the Arduino Expansion Board. The examples were made based on the Arduino Expansion Board; however they can be used with the Mini-Breakout Board too. You can change the GPIO if you want. In the example is the GPIO13 because the idea is to see the blink behavior in the on-board LED on the Arduino Expansion Board. You can use the following table to know which pin on the Mini-Breakout Board corresponds to which MRAA number: mraa/edison.md at master · intel-iot-devkit/mraa · GitHub
Regarding your second question, the blink example doesn't need any input pin. It only requires one output pin which will blink the LED.