What causes the holes and different colours when exporting FBX from Blender to UE4?

I exported my object from Blender to UE4. But after the import it looks like a Swiss cheese. It has holes everywhere and besides, where I apply only one material, suddenly two different colors appear for it, one light, one dark. I spent all day yesterday adjusting the orientation of the normals, hoping that this would solve the problem. But as you can see, the normals in Blender are now all orientated as they should be, but the problem in Unreal Engine persists. What could be causing this problem? I don’t know what to do next.