qgis - Geoprocessing tools fail though CRS same, prj-file ok, edit mode off, topology valid, etc

For my layers none of the QGIS geoproccesing tools (difference, intersection, etc. all give empty attribute tables) work, though I've checked for all (?) error sources (as in the title). Then I tried to do a manual edit of my polygon-geometry (adding a ring) and this is what happend (the data is in my Dropbox):

I'm using QGIS 2.10.0 on Win7

Answer

There's an issue with your "mair_dxf" layers. From the metadata, it reads that there's 3 features whereas in the Attribute Table, it only reads 2 features.

To rectify this, re-save the layer as a new shapefile. The metadata should read 2 features now, run the Difference tool again:

Hope this helps!

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Edit:

Turns out that there is an issue with QGIS 2.10 where the layers fail to be processed correctly. However, the layers work fine in QGIS 2.8.2 and 2.12.0 where I was also able to add rings successfully: