Is this normal for growing baby duck?!?!?!?!?

ok. i found a group of baby ducks and its mother behind my house in the desert not near any water. so we catch all the baby ducks and then try to catch the mom duck. but she takes off. and we tryd for about maby 2 or 3 hours. well there was 8 baby ducks and now there is only one. my baby duck. and she is a female mallard duck and she has grown alot. over the past month. we give her a diet of eggs, vegitibles, cheese, bread. as she is growing she has a bald spot on her back but feathers are growing everywhere els/ she has fuzz still but feathers too. she picks at her back alot and the rest of her body as well. but every time i c her she is messing with her back mainly after baths. is this normal?? and will she grow feathers on her back?? im letting her go when she grows a little bigger. {back to apolo park where i think she came or her mother} but yeah. please help me out. :/ i love this duck so much and i hope she is ok.