I’d probably use the natural tag, there are other natural dams created by earthquakes, lava flows or travertine terraces for example perhaps natural=dam

Looking at the help, it looks like you should use waterway=wadi as this “stream” is mostly dry except after rains…

waterway=wadi

The OSM example has the school as an area around the various school buildings. Each building should be tagged building=school.

Certainly in the warmer US states you have a few buildings for sets of classrooms, offices, gyms. In colder climates they tend to have only one building.

So the area around the buildings does seem to fit best in warmer climates.

OSM example … amenity=school