A 3x3' coop is not nearly enough room for 4 full grown hens. Recommended minimum space is 4' square per bird inside, and 10 square feet per bird in the run. These are merely recommendations, and not a hard and fast rule. But over crowding can cause bad habits like feather picking to occur. Here is a good article by Ridgerunner on space for chickens:
https://www.backyardchickens.com/articles/how-much-room-do-chickens-need.66180/
If they're not out free ranging, they need food available at all times. Not enough protein will also cause feather picking. Tell your teacher to use the PVC feeder - it will reduce feed waste.
To "cull" simply means to remove from the flock. It can mean kill, sell or give away. It's perfectly fine to cull a bird that's no longer working in your flock. The good of the whole flock needs to be considered, along with what keeping that bird may cost you. If she's stressing the other chickens so they're not laying, it's costing you money to feed non productive chickens for nothing in return. If she's injuring them, you may have treatment costs. If she's attacking people, she's a liability. If she scratches someone and causes an infection, that's going to cost the school. These are all things that one needs to consider when trying to decide if they should keep or cull any animal.