Thanks again for your effort. I already got it working with your first provided example. Please consider this ticket as already solved and don't provide any further examples or videos. My last answer wasn't a programming related problem, just a suggestion.
Because whenever I declear the DataContext within the xaml, I don't have to set anything code behind. So, I am aware that setting the DataContext in the xaml.cs after the control has been loaded, works. However, from my point of view I can't understand why this is still required, since the DataContext is already provided in the .xaml. So I can just assume, that your TreeViewAdv.ClientControl lack some features.