There’s something very wrong with that mesh. When you go to edit mode, the median Z value of the selection is NaN. That’s why scaling doesn’t work. (Median being NaN suggests there’s at least one vertex with coordinate(s) that somehow fell out of range of values that can be represented, it’s “not a number - NaN”). If you select all faces, the median will be NaN for all three axes. Something somewhere went wrong with coordinates. There are also zero-area faces, loose vertices, etc…
There is a way to “fix” it: go to object mode, open the Python Console in one of the editors, type this:
and press Enter. It should print “True”. Now when you go to edit mode, there will be 2530 vertices at the origin with lots of edges stemming out to the model. I think you can just delete those vertices. Whether this ruins some other part of the mesh, I can’t tell. But at least it lets the tools work again.
How did you get this mesh into Blender? Some sort of importer?