I don't know if all the claws should be black? But, from the picture it doesn't look unhealthy to me. Rowdy has one that's just the tiniest stub because one of her parents bit it off when she was a baby. She also has no pain or anything with it, so I wouldn't worry about it. It happens fairly often to baby birds when they are still in the nest box.
If you are going to cut them yourself, I would recommend having a helper. One of you can hold the bird while one holds the foot and cuts each nail. Try not to go too short and have some Quick Stop or corn starch nearby in case you cut one too short and need to stop the bleeding. It can be hard to do it all by yourself unless your bird will stand there for you cooperatively so you have both hands to handle the foot and cut the nails.
I did do a sinus flush on Merlin by myself the other day, but it was hard, and I probably should have waited for my neighbor to stop by and help. I bet for sure next week I will need another person as she will remember what happened and be less cooperative I bet.