I have one that has a Cross Beak.  He is also missing an eye which can be common as it is a malformation in the skull.  Mine is robust, happy and (I tell him all the time) very handsome.  He is a Barred Rock and almost 8 lbs.  I regularly trim and/or file his beak.  As a baby, when the beak is VERY soft, I used kitten nail trimmers (not dog, too big) and took just a tiny bit off, then filed with an emory board.  It is good to get them used to this at a young age.  Be careful to do in good light so you don't "quick" the beak.  It will bleed horribly.  Have some blood stop on hand when you trim just in case.  Because of the malformation, mine's beak was a bit brittle on the top where it curved and one day he must have knocked it into something because it broke.  Awful thing, I had to handfeed for a day because it was so sore.  FYI:  ambisol for sore mouth/gums on people works well in this case to numb it.  
My roo's beak was similar to yours at that age.  As a baby, I made him a damp mash to choose from with the dry chick starter.  I also supplemented him with polyvisol vit for the first 1-2 weeks.  As an adult, he needs a deeper food bowl and I use a rubber feed bowl from the farm store.  He needs the deeper bowl to be able to scoop.  He cannot pick things up like a seed or bug off the ground and this is a bit sad, but really he seems a happy bird.  He likes treats with all the others and especially raisins.  I have learned how to give his couple raisins to him by holding him in my lap and he tilts his head a bit while I pull on his wattle to open his beak and poke it in the corner of his mouth so he can get it.  I have several special needs birds and do not breed.  1. Because there is always another bird around the corner and 2. I want to be responsible and not breed genetic defects.  Keep this in mind.  Also, your chick will not be able to peck you much when he gets older, or defend himself with his beak so may need some special watching.  This is good in a way for you and the hens, if it is a roo, because his pecks feel like him bumping against my leg and he will have difficulty grabbing on to the girls for mating.  Mine has learned he has more to grab on the hind end of a hen with her tail feathers and does the deed backwards.  I keep telling him it doesn't work that way, but he doesn't seem to care.