Well, since this has been resurrected and I missed it the first time - Your cat's claws are absolutely normal. The dark you see within the nail is quick, the blood vessel. And the dark you see under the nail is dirt from her scratching in dirt to cover her bathroom spot or maybe tree bark from sharpening her nails.
You WILL see bits of nail shredding off. As she sharpens her hooks the old nail is peeled off.
The quick WILL recede if nails are cut a bit shorter each time or too short.
I hope your Vet did not sell you that stuff you were putting on her nails. If so, time for a new Vet.
I don't need to cut any of my cats' claws. They do a good job of keeping them short on their scratching posts. Sometimes you have to experiment to find a post they will use. Some cats like the post vertical, some like it horizontal and on the floor. Some like carpet with carpet side out and some like carpet with the jute backing side out. We have the tops of cedar fence posts that nearly all our cats like, the cedar is soft enough for them to dig into it.