It seems my Arduino doesn't work
It looks to me like your arduino is working just fine.

In the first two images you use the arduino only to provide 5v power to the circuit on the breadboard. In the first image you haven't connected your button to properly function as a button. I don't know the exact pin layout of the button (which should be explained in a datasheet of that button), but it is also good to know exactly how to holes in a breadboard are connected. This picture shows why your button works on your second image but not your first:



This picture also shows how the breadboard holes are connected:



In your third image you have practically connected input pin 13 to GND, so it makes sense that digitalRead(13) in your code always returns LOW. Thus, the variable var is always LOW (or 0). Thus, the comparison (var == HIGH) is FALSE, which won't send "OKAY" to the serial monitor. And, the comparison (var == LOW) is TRUE, which will* send "OKAY" to the serial monitor.

I hope you can follow the logical steps and it is clear to you what is happening.