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How much does lack of an atmosphere and the moon's material affect the lighting?

You can see from the image - in spite of the bright sunlight the sky is black, because there is no atmosphere to refract and reflect the sunlight like on Earth. For planets and moons with no atmosphere, the sky is perfectly black both day and night.

But why is the astronaut's shadow on the ground so dark

There is no ambient light from the sky, so nothing to soften the shadows, except perhaps some earthlight, but that's not especially bright.

but the front side of the astronaut, which is equally hidden from the sunlight, is nearly as bright as in a CGI image rendered in "no shadows" mode

The surface of the moon is mostly a fine sand, with lots of diffuse reflection. Surfaces above the ground are strongly illuminated by this reflected light, even when in complete sun shadow.

By the way, the moon moves in 'synchronous rotation' with (or: is 'tidally locked' to) the Earth, meaning that it rotates around its axis in the same time that it takes to orbit around the Earth, and in the same direction - anti-clockwise when viewed from the North. This means that we only ever see the same face of the moon, as I'm sure you already knew (although due to lunar libration it appears to 'wobble' by several degrees N-S and E-W, so that we get to see up to about 59% of its surface over time).

This also means that when viewed from any point on the moon the Earth doesn't move around much in the sky - only a few degrees over time due to lunar libration. It doesn't rise and set like the sun and moon do when viewed from the Earth. Any references to 'Earthrise' or 'Earthset' on the moon are from the viewpoint of an orbiting craft, not from a point on the moon's surface.

Is this an Apollo 11 photo? If so, the Apollo 11 landing site was in the Sea of Tranquility around 24 degrees from the central point of the moon's visible face. This means that the Earth would have been at an altitude of around 66 degrees, not on the horizon.

EDIT: I just read the above post.. so it was Apollo 16, not 11. The Apollo 16 landing site was somewhat closer to the centre of the moon's face, so the Earth would have been at a higher altitude.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)