Does using brightness dimmer (screen filter) really save battery? We know that the lower the scree light/brightness, the lower the battery consumption.

There are some applications which provide ability (without root) to lower the brightness beyond the (default) limit.

So, I want to know does it really save battery? In other words, does it affect battery consumption comparatively to default minimum limit?

Btw, I'm also interested to know how does such application do this task if going beyond limit?

And is there any command-tool related to settings brightness level?
When you decrease the brightness of a light, it normally means less power is consumed. Therefore, having a lower screen brightness than your default would suggest battery use is reduced further than normal.

As far as I can guess, the screen brightness will just be a command in the android system that changes power flow through the screen LED's. The phone manufacturers likely just set their brightness slider's lowest value to whatever arbitrary value they expect a standard user would require. The app's that you are using just influences the same function, but drops the power lower. 

e.g. 
Samsung use a minimum screen brightness of 30% power, but your app will drop to 10%

I don't know the specifics of such tool.