In my test such issue does not occur, the UXComboBox will have the correct SelectedValue when bound properly. Attached is the test page I am using for this scenario.

By default the command will be called when a new window is opened or upon invoking RearrangeWindows method in UXDesktop

Based on my discussion with the developer it seems this issue is caused by a bug. A bug report has been submitted to the developer.

In such scenario, you will need to bind the CommandBindingCollection object to the element which implements the command.

In your attached sample, the element which has the minimize and close command is UXWindow so you will need to bind the CommandBindingCollectionto UXWindow. Here is the snippet:

public class SymphonyUXDesktop : UXDesktop
{
    protected override DependencyObject GetContainerForItemOverride()
    {
        UXWindow newWindow = new UXWindow();
        newWindow.IsClientVisible = true;
        newWindow.CanMaximize = true;
        newWindow.CanMinimize = true;
        newWindow.CanMove = true;
        newWindow.CanResize = true;

        CommandBinding windowCloseCommandBinding = new CommandBinding(WindowCommands.Close, HandleWindowCommand, CanHandleWindowCommand);
        CommandBinding windowMinimizeCommandBinding = new CommandBinding(WindowCommands.Minimize, HandleWindowCommand, CanHandleWindowCommand);

        CommandBindingCollection bindingCollection = new CommandBindingCollection();

        bindingCollection.Add(windowCloseCommandBinding);
        bindingCollection.Add(windowMinimizeCommandBinding);

        CommandManager.SetCommandBindings(newWindow, bindingCollection);

        return newWindow;
    }

    private void HandleWindowCommand(object sender, ExecutedRoutedEventArgs e)
    {

    }

    private void CanHandleWindowCommand(object sender, CanExecuteRoutedEventArgs e)
    {
        e.CanExecute = true;
    }
}

Based on my test, the method runs without any issue on button click event handler.

After discussing this issue with the developer, it seems the method will always return  empty image under custom converter because in the converter state the window will not be displayed.