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Hello,
I have a question for you about GUIs. You made a window (the parent window), but you want to add some information to it so you create a child window. My question is how do you restore the parent window image that was covered by the child window when you close the child window? Do you copy this portion of the parent window to a secure memory location than restore it completly when the child window is closed or partially when the child window is moved or there is another method?
Thanks for any help.

There are many different ways to handle this. I'll just list some of the AmigaOS options so you get the idea.

SimpleRefresh - when parts of a window become uncovered, you signal the application to redraw its entire window. That's simple, but slow.

SmartRefresh - when parts of a window become uncovered, you signal the application to redraw the uncovered parts. Fast but a bit more complex.

SuperBitmap - The OS holds a complete window image in some memory area, and when parts become uncovered, copies the affected memory region into the screen display. Fast, no context switch, but eats lots of memory.

There are many other architectures possible. It's a matter of who has the data to do something, and who knows what has to be done.

Hello,
I have another question about GUIs. How are the controls (message boxes, edit boxes, buttons, ...) drawn? Do you draw it line by line and pixel by pixel or there is another better and faster method?
Thanks for any help.

If you're thinking about some way of hardware support for UI primitives by the GPU... I don't think there's such a thing.

Other than that, it's basically your decision how you handle UI primitive drawing...