Sorry in advance for being concise, I don't have much time right now. Feel free to ask for clarification.
You can probably separate the tabs into a simple ListView (just hack it so that it looks like tabs), and then load the content of a given tab with Loader (or use States if you prefer)
I don't understand this bit, but I haven't read your post fully. Maybe I'll get back to this later. Just a hint: KDE project probably has some ready-made breadcrumb components.
OK this is quite complicated territory. I advise going step by step, carefully reading the documentation (it's really good, but it's hard to wrap your head around some concepts). Start with a simple QStringList as a model (just to get a feel of how it works) and then slowly start adapting your code so that it can handle your data models.