Chick starter or grower has the right amount of protein. That is part of why it does have more protein than layer feed-- they need to grow their bodies and lots of feathers in those first months.
Yes, they are molting.
Chicks molt quite a few times as they grow up, before they settle down to the adult pattern of (usually) once a year in the fall.
Chicks usually molt gradually, so they do not have bare spots.
Some adult hens molt gradually too. The ones with big bare spots are just the...