That looks like a horizontally-compressed Plate Carrée projection of about half a hemisphere. In this one the azimuth axis is squished by a factor of two compared to elevation (90° change in azimuth is the same length in the figure as 45° change in elevation in the figure); in a true Plate Carrée projection, equal angles in both directions would be represented by the same length. Since it's a projection of a sphere onto a plane, it suffers distortion problems like you get when projecting the spherical earth onto a flat map. The direction of the shortest distance between widely-separated points (or, sometimes, even closely-spaced points) will be wrong except in specific cases.
That is how the moon appears for the various elevations.
That's a flat-plane representation of how the moon appears for the various elevations and azimuths. Since it's a representation of a spherical coordinate system projected onto a flat rectangle, it's distorted.
Apparently you are still confused by that. Or still claim to be. So now we know that much.
It's a depiction of the Moon Terminator Illusion.
There is no illusion. You think there is one because you don't understand what is plain to see, and present illustrations that you also don't understand to "prove" your case when, in fact, they show that you are wrong.
If you want to claim that the moon is projected onto a dome, and that is what causes the moon terminator illusion, why don't you come up with a theory of the earth where we all live under a planetarium dome that can explain it?
No, I don't claim that. You seem to be perplexed by the concept that a coordinate system that describes positions in terms of orthogonal angles from a point is a spherical coordinate system.
The moon is seen in the sky, and it points upwards away from the sun. Why does it do this? It can even happen when the sun itself is below the horizon.
That's easy! It'as not "pointing upwards" (at least your example below doesn't) and doesn't "point away from the sun".

The sun is below the horizon, yet the moon is pointing away from the sun and earth. Please explain this using the geometry of the Round Earth model! Where is the model? Why can't this be explained?
Easy peasy! The arrow in that image is in the plane of the image, but the direction of sunlight illuminating the moon isn't in that plane. It's from behind and to the right of the camera.
Here's that same image with the approximate location of the subsolar point on the moon indicated. The spot was "eyeballed in" and isn't guaranteed to be exact (but I suspect that arrow is similar) but should still illustrate the point.

Anyway... the sphere that the surface of the moon is projects as a circle on the plane of the image, but the point on the surface of the moon that the sun is directly above is closer to you than the center of the moon, so the direction to the sun from the center of the moon is out of the plane of the photo, over the photographer's right shoulder, and directly toward the sun, whether the sun is below his local horizon or not.
There is no illusion. Confusion on your part isn't illusion, it's just confusion.