Definitely a cockerel, sorry. One of the four Barred Rock pullets I ordered this spring turned out to be a cockerel as well. Barred Rocks can be sexed by color once they have feathered in. Pullets are blacker, cockerels are more silver.
I've seen that beak thing happen in my own flock occasionally. I'm not sure what causes it, but I'm guessing probably pecking on hard surfaces, e.g. scratch grains on a concrete sidewalk. The handful of birds I've had with that all healed on their own, with no infections or anything, and still managed to eat and drink just fine. I can't remember if any of them grew their beak back or not. I don't think they did.
ETA: I doubt they grow the beak back. Commercial layers are debeaked as chicks, very similar to your cockerel, and the beaks don't grow back.
