My draw type is not on wireframe but all I see is this:
What can I do to fix this?
edit: Link as requested
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It's very hard to understand how your models managed to end up like this but the reason they appear like that and don't render is because they have no faces. Blender won't render lone edges or vertices. Tab into Edit mode and select
4 vertices on any of the objects and press F to create a face.
I would recommend recreating the scene instead of trying to fill in the missing faces.