Hi Satellence,
For reference to your first question regarding HLODs, they currently do not support dynamic shadowing, but there is a feature request in the ToDo list of things with UE-22627.
As for your immediate issue, I have a simple scene I’ve setup just for testing and when I disable HLODs in the World Settings, I will need to rebuild the scene before the change takes effect. Have you rebuilt your scene since disabling HLODs?
If you drag another static mesh in your scene, like the ones pictured in the second image, into the scene does that one stay shadowed?
Let me know.
Tim