I didn't read all the posts, just the last question.

can't I separate logic and gui when using Qt ?
Of course you can... Qt does it with the MVC architecture, for example. There are other ways too.

I'm not sure what CompView is supposed to do, but it doesn't look good. Having an object inheriting from a GUI class and a class that implements app logic is not called "separating logic".
Actually, there's a word for that: "mess". In the end you'll end up with an object that exposes both things anyway.