I see from your last screenshot that you have both ArchiCAD 13 Library and Object Library 13.lcf loaded.
LCF is the extension of so-called Library Container Files (LCF). These contain all the objects that you can place in your projects. This is a good way for shipping libraries since they are all in one file instead of being thousands of files.
The ArchiCAD 13 Library contains this Object Library 13.lcf PLUS some other folders containing background images, textures, Lightworks related stuff etc.
If you load the ArchiCAD 13 Library, all subfolders and files within it will be loaded, including the Object Library 13.lcf.
So in this case you have the Object Library 13.lcf loaded twice.
So you should go to the LIbrary Manager Dialog, select Object Library 13.lcf i nthe list and remove it from loaded libraries. It will be loaded with the ArchiCAD 13 Library anyway.
This should take care of those duplicate parts error message.
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