What exactly happens if I use an external software to clone an existing Black Kyurem? Does it break the game or something?
Nothing happens if you have two of the same form. The reason it's not legitimately possible is because the game has to keep track of which Pokémon you fused to recreate it when you undo the fusion, and it only keeps track of one fused Pokémon at a time (well two, one for the Kyurem fusions and one for the Necrozma fusions). Having both forms at once does create an issue where you can defuse one into the wrong Pokémon (because the game just retrieves the previously fused Pokémon data regardless of which form is being defused) but that's not really game-breaking, just mildly amusing.