To expand on Arnold's reply, Web Mercator is designed for viewing and ease in creating/storing/retrieving cached imagery tiles. It's not designed for calculating distances or areas (if you get correct answers, then the software is calculating in something else!).
The fact that the points all lie on top of each other is due to the project on-the-fly capabilities of ArcMap. Whichever coordinate system (CS) the data frame (map) is using, any layers in a different coordinate system are being converted in the data frame's CS. (1)
You have a weird case, in that WGS 1984 Major Auxiliary Sphere isn't a "real" geodetic GCS (datum). Coordinates are the same as in WGS 1984, but are treated as if they're on a sphere with radius 6378137.0 m. If there were two or more geodetic datums involved, you would need to pick transformations. However, ArcMap will still project on-the-fly even if you don't set any transformations. Basically, it just skips the transformation step.
Notice how the longitude lines are parallel in Web Mercator. As a rough guide, that means that the true east-west distance is about cos(latitude) of what's reported. This fits well with what you're seeing: 99/138 = 0.717, cos(44) = 0.719.
You're much better off using the UTM zone, or possibly switching to the SPCS zone (although that's not on WGS84).
Melita
(1) If you want to see what the data looks like with project on-the-fly turned off, click the globe on the Coordinate Systems tab of data frame properties and select the Clear option.