Is the fireplace damper open when the slide is to the right side or left side?!!

Usually, to the right...in my experience. You can confirm your setup by putting a flashlight in the fireplace or by lighting a fire. You should very easily see the light from either as the damper opens. The Fireplace Screen Damper is your brake peddle.

- So, only open the damper enough for the fire to maintain itself with a moderate flame. You'll get a good and complete long-burn and not a "roaring" fire that goes through wood or synthetic logs very quickly and inefficiently.