Re: Is my conureās cracking/peeling beak normal?
Looks like your Parrot has been busy working on cage bars /perches or hard toys, etc... This is not uncommon as a general statement. Remembering that the Beak grows from above and down to the wear (work) area. Over bar or perch working can damage the Beak faster than it grows. That is when you want to involve your Avian Vet. It is one of the reasons, I recommend regular Vet visits. I'm not seeing that at this point based on a single photo.
Consider adding soft pine (possible thinner) wood toys.
But as Major TOM stated, looks fairly normal.
Re: Is my conureās cracking/peeling beak normal?
Indeed it is okay, when your Conure uses his/her beak a lot, it may peel. It happens to my Conure, but when it does, I take Birdo to Simbadās (a local bird store) to have her beak filed and smoothed, and her nails clipped. It doesnāt bother them, their beak is like having a big, dangerous nail on their face.