No need for boards or supports, just stack the dummies and decorate them. Attach them together with tape in between them, or royal icing or melted chocolate or staples or however you want to do it.
I would definitely use a board under the stacked cakes, because it would look more like a real cake - you could decorate the boards edge with ribbon to make it look more believable but the most important point is moveability. without a board you have nothing to hold onto when moving the cake and may leave marks in the icing.
Are you talking about a board under the base cake? Yeah, you need to carry it around so put it on a base board.
AIf you're doing a normal stacked cake there's no need for boards inbetween (if you're covering with sugarpaste, no idea about buttercream).
You will, depending on your design, still want a drum under the base tier, but as you don't see the boards on the other tiers, and the dummy is solid so just holds the weight of the next tier quite happily, why spend extra time and money.
If you are doing a traditional cake with pillars, you'd use a drum under each tier but that's for aesthetics, so still no need for a supporting board.
ADummy cakes are made from styrofoam, so they don't need boards or supports when you stack them up. You should put a cake drum under th bottom tier so that you can carry it around. Buttercream isn't hard on styrofoam, it doesn't corrode or dissolve it, you just won't be able to re-use the dummy without a huge mess if that's what you like to do. You can also use royal icing or the stuff that they sell to ice dummies, which is basically like spackle. Those dry hard and are more permanent than buttercream.
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