False Positives can be mostly mitigated using historical data. If the child is consistently meeting alert criteria at a specific time (ie. Mon-Fri at 1300-1330 for Recess), alert is logged but no notification sent, unless toggled otherwise.
The real challenge is the power consumption. Consistent monitoring burns a lot of power, someone smarter than me should figure it out.
Garmin Bounce [0] has some of the features on your list and many more (like on-watch LTE). I don't believe it includes the ability to use heart rate and stress levels to trigger automatic alerts. I have no first-hand knowledge in this field, but I would imagine it would be very difficult to implement this without many false positives especially for kids in the day care and school settings because excitement and play likely look very similar to anxiety and distress from the point of view of the heart rate sensor.
0: https://www.garmin.com/en-US/p/714945/pn/010-02448-02/