Normal soul gems are considered "tainted" when turned black via magic as its an unnatural process. There still had to be normal black gems for the fact that in order to know that black soul gems existed and normal ones could be converted. That is to say if there were none in nature, then how would anyone know they could exist? Natural ones are extremely rare, so thats why most ones you find (in the lore) are magically changed ones.
No that is not true.
Black soul gems made their first appearance in Oblivion, where the only way to create them was with a ritual at the Shade of the Revenant.
The Shade of the Revenant is when Mannimarco eclipses Arkay.
The souls of the playable races cannot be soultrapped because they are under the protection of Arkay.
That is how it worked until Mannimarco the necromancer achieved Apotheosis and became a god during the events of Daggerfall.
Now the moon Mannimarco (his divine form) orbits the plane(t) of Arkay (the Aedra are planets in the sky) and that causes an eclipse every 8 days.
During the time of this eclipse black soul gems can be created via a ritual.
Mannimarco flaunting the edicts of Arkay.
That you can mine them in Blackreach must be an oversight.
Or, maybe, during the 250 ish years since Mannimarco's apotheosis his influence on Tamriel has gradually saturated it until black soul gems occured in geode veins.
But that is something I just made up to explain away this oversight.
There is no evidence to suggest a soul is destroyed when trapped and used for enchanting purposes.
We do know that a trapped daedra soul in Daggerfall was released when an item enchanted with one broke, and it would spawn behind you and attack.
I think that due to the lack of evidence that (white) souls get destroyed, youd think it would be mentioned somewhere as evil, they transfer to the Dreamsleeve when its charge is used up.