If they were really 7 weeks old they would be 90% fully feathered. The people you bought them from seem misinformed or they were too busy to keep track of the well being of the chicks.
Did you buy the chick?
Looks about 3 weeks old, cemani or svart hona.
Make a small amount of feed mash for the chick, it's easier to digest. Feed mixed with water then stir to the make it look like oatmeal consistency.
You'll need to monitor it's condition give it some warmth.