broken

Hey everyone, I've got a couple of quick questions. My grandmother has a couple of nails that split vertically from the free edge, and nail treatments and moisturizing has only done so much for her. (I would upload an image, but apparently it's too large.) My first question is: Should I go with...

So attached is a picture of my nails. One of my nails broke so I took it off, because I find the salons I go to to be very rough on my nails. I noticed discoloration which I thought might be mold. The finger next to it was also feeling sensitive so I took that nail off as well. What I found is...