4 week old Black (Mystery Breed) chick dry feathers

[StephanieRose44]

My blackbird (chick) Idk what kind of breed he is I got him from a chicks store that later found out the owner doesn’t know what he has or he gives people a lot of roosters claiming there hens. But besides that he is a sweet bird and he loves to lay under the heat lamp and stretch his legs out it’s funny to watch, I’m not sure if this is the reason but he’s always layed under the lamp. This morning when I came in to feed them I noticed his feather feel very dry not smooth and shiny. I know he’s probably starting to loose his baby feathers and I know what that looks like, but is this normal if not what can I do?

 

[StephanieRose44]

Here are some more pics if her/him.

 

[Fishkeeper]

Do you only have one?
Is he normally active? He shouldn't be lying around all the time.
What are the temps?
What are you feeding him?
Can he access food and water from under the lamp?