My Sun's beak peeled all the time when I first got him, I don't think it's a big deal, though I never really looked up anything on it.
For the picky eater thing, you could try making him a mash and mixing it in with his pellets one day.
I take kale, jalepeno, apple (his favorite), raspberries and carrots and put them all in a food processor till they're about bite size and give it to him. He was hesitant at first, but now he loves it! Especially the carrots (and I used to not be able to get him to eat those for anything!) I freeze it in ice cube trays and defrost one each morning. I also do a mix of lentils, garbanzo beans and quinoa pasta!