If you mean a school nurse or counselor that is employed by a public school- no. Just some person volunteering and working with kids is not held to the same standard, so probably won't get in much trouble if they spill the beans. Note: if you pass on information that concerns the safety of others, then they are obligated to report to the proper persons.
yes, because they may not know how to deal with the situation and b, because their worried for your safety or well being.
ps..its called being concerned
Legally yes, ethically probably not.