Backdrop means you can see into the void. If no skybox is present in the map this is going to result in these smears where the last frame something was rendered in the void is just going to stay.
Like this:
If a SkyZone is present, instead of having nothing to render there the game shows the view of the skybox through the SkyZoneInfo actor, with the same angle as the player's vision.
I.e. shows the sky.
A surface isn't backdrop. It's a surface. But you can let it "fake backdrop", i.e. act as if it was backdrop, and thus showing the Skybox.
Now for the lights.
A sunlight can't just "shine", that's not how they work. They're not like the lightbulb lights that emit light on their own. It needs visible sky (see above) to shine
from. The sky is going to emit the light (in parallel rays, as you noted) from the same angle as the sunlight actor points at the SkyZoneInfo actor.
E.g. your sunlight is pointed west, it's going to hit the map from the east.
To make this work, technically only the eastern side of your "world cube" has to fake backdrop. If you want the sky to show up on the others too you'll have to have them fake backdrop too.
The bottom may not be mentioned because whoever wrote what you were reading assumed players aren't going to see it anyway, e.g. because terrain is going to cover the ground. If you're building a floating space-station where players can look down through glass windows in the floor of the station, you're going to need your world cube's floor fake backdrop too, of course.
But the light is still only going to hit from the angle it's pointed from.
Sunlight actor in the Skybox makes the sky emit its light. Period.
A sunlight placed in the map area itself, not in the skybox, makes the sky emit its light
but only into the zone this sunlight resides in!