Display properties window on default

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Short answer: unfortunately no.

Long answer: no, but maybe you can hack the source code. It's in the modules/highgui/src/window_QT.h and windows_QT.cpp file.

I think it's possible to create a function to get the pointer to the property window in windows_QT.cpp:

CvWinProperties* getPropertyWindow()
{ return global_control_panel; }

and add the function header to the windows_QT.h file

In your program you can call this function to get a pointer to the property dialog:

CvWinProperties* propwin=getPropertyWindow();
if ( propwin != NULL )
    propwin->show();

You should call this function after the creation of the first window (that's when the control panel is created).

Disclaimer: this is an untested method, do it at your sole responsibility. If you want to play with the source code, better know what you are doing.

That said, it's not perfect, so you can modify it to make it better, that's why OpenCV is open source.