Is there a way to hide it? or to make it transparent? or to make it open with the same size always?

there is a whole section in the manual about advdispwhy would you hide it? transparent? - noif you make advdisp the right size, put it on the panel just the way you like it, adjusted the font size, background color, font color, etc, right mouse click and save

Like the default FS2002 ATC Transparent Window. You can show it or hide it. It would be just great to have the same ADVDisplay for all panels in the same place, and transparent so it doen't interfere with the view.