I honestly guys have had amazing results with a meringue buttercream. Withstands handling well, I can really work it and smooth it when it's chilled. Although I suspect any all butter bc would work honestly
For 3 6" cakes I would use about 4 dowels in each of the bottom two cake, I tend to be on the side of using more than I probably need.
I would definitely say the dowels were your problem you need dowels anytime you are stacking more than 4" of cake no matter what the size. winniemog gave you an awesome reply that's more in depth
My guess would be they used a machine of that kind. I GUESS you coukd use an exacto knife and a paper template on top of black gumpaste? I'm not sure how precise that would be though.
When I did this I used my silhouette cameo machine.