I have no idea. I suspect a lot of the tasks you are asking about are automated features of Power School of what ever software the school.
I would assume the teachers do their own setup, here they get 1 period prep time 4 days a week, and every Thursday is a half day with the afternoon being teacher prep.
Kids here now all have to go a a central location to signup for school so I suspect student health records are kept there. One factual piece of information I did find the addresses on question, each school has a "designated school employee" for the administration of medicines.
http://www.sanjuan.edu/Page/3996
When my kids got sick, the Principal always called.
I don't about schools, but being involved in youth sports, making sure someone is calling 9-1-1 is part of the training we get as part of the initial evaluation of an injury. In Little League, the coaches are to attend to the injury, the umpire is in charge of making sure medical help is on the way. Our fire department has made it clear, it is never a waste of their time to respond to even a minor injury to a child.