Not sure what to tell you. The TD only tries to access the active Data Store folder. If it is unable to find the folder, then it won't be able to access the player database. This is the main issue, and there's no way around it except to switch to a known, existing Data Store, which it does. I do not know why upon startup, and upon trying to activate a particular Data Store, that the software is unable to locate the Data Store folder, but if you edit the Data Store path it is then able to locate it.
Regardless, the TD is only asking Windows, so Windows is telling the TD that the folder doesn't exist. So this would seem to be outside of the control of the software.
Also, something caught my eye: in the 4th screenshot where the folder browser is displayed, those 3 mapped drives (music, photo, and Privat) each have a red X on the drive icon. This usually indicates that Windows is unable to connect to the mapped device (at least that's what I think it means). I have no idea why you are clearly able to browse one of them if Windows thinks it cannot connect. But this might be an indicator that there's another problem.