Looking for mites/lice is not fun at all, especially with such a tiny coop.
Easiest if you have someone to help, they hold the bird, you part the feathers.
I do it alone at night with a headlamp, but I have a large walkin coop,
can grab the bird off the roost and sit down in a chair with bird on my lap.
Also, wipe down underside of roost with white paper towel well after dark,
look for smears of red from well fed night feeding mites.
16% protein is about the minimum for layers, adding any other foods/treats dilutes that protein.
You might want to think about switching to a higher protein all flock/grower/finisher.
lots of different names so start reading labels of what's available where you buy feed.
My Feeding Notes: I like to feed a flock raiser/grower/finisher 20% protein crumble to all ages and genders, as non-layers(chicks, males and molting birds) do not need the extra calcium that is in layer feed and chicks and molters can use the extra protein. Makes life much simpler to store and distribute one type of chow that everyone can eat. I do grind up the crumbles (in the blender) for the chicks for the first week or so.
The higher protein crumble also offsets the 8% protein scratch grains and other kitchen/garden scraps I like to offer. I adjust the amounts of other feeds to get the protein levels desired with varying situations.
Calcium should be available at all times for the layers, I use oyster shell mixed with rinsed, dried, crushed chicken egg shells in a separate container.
Animal protein (mealworms, a little cheese - beware the salt content, meat scraps) is provided during molting and if I see any feather eating
