I think it’s black tourmaline. The second photo you posted looks exactly like a sample that I have, and like the photos in a book I have by Scott Cunningham who was a brilliant stone/crystal expert. You can ward off nightmares, and encourage good sleep by putting it under the pillow, or (this is something I didn’t know!) if you are afraid of being found out and need to hide your spell work, you can put under the mattress for better hiding. Back in the day, people frowned on that sort of thing, so you had to hide things you used in interesting ways. Black tourmaline is very good for insomnia as well. I think it’s wildly interesting that Nana was into ‘witchy’ things! Did she ever talk about it at all, much? Do you feel like she handed down her skills to you, ever? You should read some books and articles. Maybe you found this for a reason, to encourage you!? Good luck!