How to regulate a led on-board? There is blink project consisting 3 sections: 

1 - regulation of the led brightness using a potentiometer

2 - whenever: the button is pressed - the led is on

-   the button is released - the led is off

3 - change state of a led statically

The question is that:

May I make this project on-board?
I am curious that, if I will try making this project on-board (Arduino UNO) will the Arduino damaged?
Pin 13, which is the on-board LED, is not a pwm pin. So you cannot Control the brightness of that LED on-board. You will have to use another LED and a PWM pin.