It was only three obj files so I can't say anything about the levels but you mentioned that it was intentional so that should be ok.
Next time don't forget the mtl files that go with the obj files. Without it Sweet Home 3D will import an object with a single gray material named "default".

The white corner problem is easy to solve:
When you export you can choose Export all or Export selection . You exported all, which means you also export the ground and that is the white corners you see.
Select the parts you want and export only the selection.

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