Moved apps to SD. SD was full, Apps are vanished now, but phone storage stays clogged. What should I do? Phone: GT-I9100
A: 4.1.2

I tried to move Apps from my phone to the SD card with root permissions enabled.

I missed the point that the SD card was running out of space during the process. A warning did not take place. 

Afterwards the Apps seem to have been disappeared, but the Phone storage is still clogged with only 200 MB free. I thought that I could perhaps reinstall the broken apps to make them available again and move them again when the SD-Card is cleaned properly. But this seems unviable because the phone claims about missing space every time I try to fetch the app from the store. 

If I enter the setup section for memory it takes eternal to sum up the memory consumption for the different categories (apps, pics/videos, audio, downloads and so on)

Questions:
Is it a valid assumption that due to the failed move to SD card the apps got rendered disfunctional but are still lingering on the phone memory? How can I verify that and what to do then?

What might prevent the phone to calculate the memory usage in finite time?

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Sometimes the OS misinterprets files inside of the sdcard. However, it is possible that the applications failed to move. I would suggest trying to try reading the contents of the sdcard from another device (another phone or computer). Then try seeing if the applications are in there. If they are, chances are the sdcard isn't mounting properly. I would suggest backing up the sdcard and then formatting then restoring the files. After doing this try inserting the sdcard into your phone again and see if your applications load.