The Black Dragon when flying is like a Lich, but when on the ground...well it follows the same rules as other ranged units or regular dragons since I've had it drop before reaching Claudia and even when its right next to the healer group it ignores them and just wants Claudia dead.
Am I right on that second part? Hard to say since I'm just observing what I see.
As a word from the wise, the healer in charge of keeping the Witches on the top alive should have her skill on until you can place the bait unit in the west region of the map. Just to make sure beyond a doubt Calliope stays alive.
The exact drop rates for the fangs can of course be found on the aigis wikia, but in a 'tldr' way they are damn decent. For an item collection event. Barring the second map and Twin Dragons G, there will be at minimum 1 drop that is guaranteed to give you dragon fangs and its usually from the tougher dragon enemies.