Limit it so that user can select an Item from any category in FTV1 but can only drop it in the same category in FTV2
Probably this means that you'll require unique DragDropAcceptNames for each category.
Where a user can drag an Item from FTV2 to FTV1 and it removes itself from FTV2 but doesn't add it to FTV2
removes from FTV2 and doesn't add to FTV2. What do you actually mean?