Please advise:
1. If this is something intended
I believe it is the intended behavior. You might want to change Position/DefaultMonitor values. For instance, if you choose poScreenCenter for Position, forms should move.
Check finer details from the source code TCustomForm.MoveToDefaultPosition
2. In case I really forget to move the Form before closing on my laptop screen how I can move the Form to the laptop screen when having only the laptop
Alt+Tab to activate your application
Alt+Space to get the context menu
Choose move (m if using English interface)
Use any arrow key to initiate the movement, then use your mouse to control and finalize it.
If I save a project in Lazarus/GTK2, then re-open same project in Lazarus/Win32, all the project's forms are off screen to the right.
Sounds like a bug to me.