Site maintainer here. There is a polygon drawing tool in the upper right corner of the map. You can use it to draw polygons on the map and assign them a height. The shadows will update instantly. You can use it to add buildings that are missing from the map, simulate a tree placement or even simulate cutting down a tree if you set the height to 0.

Website creator/maintainer here. Happy to try and diagnose the error if you elaborate on what the discrepancy is (tree, building, hill, etc)...

This is interesting. Have you used it to find a nice place to have a drink?

Not specifically for eclipses but has been useful in finding places where the sun will be visible during the current eclipse since the eclipse will occur when the sun is quite low on the horizon.