is a child who had been enrolled in a children's hospital's mental health unit

considered to have been “confined to a mental institution” if the enrollment was not ordered by a court? Is it protected by HIPPA?

In what context? The fact that you used quotation marks indicates that you are trying to determine whether or not said child is affected by a law or policy.

If you are filling out something legal for something important, you need to ask an expert in your state about this. The hospital may have someone that can answer your question. “Confined to a mental institution” usually doesn’t just mean a child who has visited a psychologist or a psychiatrist for outpatient treatment. It also may not mean someone who was checked in for observation voluntarily even it was inpatient. In my experience only, that question is targeted towards people that were committed for longer term stays at an inpatient psychiatric hospital because of severe mental illness. You don’t want to just say ‘yes’ if you aren’t sure if it applies because it could trigger a lot of red tape and work on your part and others unnecessarily.