Question1:
Why GroupBox has not transparent property? How to make GroupBox transparent (by easiest way, no 3rd party components)?
as garlar27've said, unless OS supports the transparency for controls, you won't be able to enable it easily.
However you can try the following:
* setting window transparency via WinAPI functions (if you're coding for Win32), but i'm not sure if it works for a controls (though it DOES work for forms);
* read the Lazarus wiki for 3d party controls or search google;
* Instead of using TGroupBox control, you can place TImage. Draw groupbox-es (via themes) borders inside of the image, leaving the rest of it transparent for background controls.
P.S. MacOSX is full of transparent controls (no need for hacks and/or workarounds).