If it is midnight for the observer then I don't see how the observer can see something on the day side of the Earth.
Showed you how, with a series of 3D models. Have you looked at them at all?
Once again, midnight does not occur at the farthest point on Earth from the Sun, for an observer at 52 degrees North.
The combination of their latitude, along with the Earth's axial tilt, toward the left side of the sun, allows them a position with a clear view toward the Moon in the latter part of its first quarter of orbit.
How is it that so much of this fits perfectly consistently with the standard globe model, but you still deny it?
When viewed from above, with some more labels for you;
When viewed from the side of the Earth opposite the Sun;