Corrupted files on internal storage (now readonly), how to repair internal storage?
This is an answer to my own question:

I managed to fix this problem (until now), by doing following:

(NOTE: Do this at your own risk!)

01.  boot into Android and enable USB-Debugging
 02.  backup data from SD
 03.  update busybox via PlayStore
 04.  reboot into recovery mode
 05.  mount system partition (via recovery tools like CWM)
 06.  connect to device via USB + ADB(-Shell)
 07.  get internal SD device name (via mount which is for me/dev/block/mmcblk0p11)
 08.  format internal SD (via mkfs.vfat -F 32 /dev/block/mmcblk0p11)
 09. check new formatted partition (via fsck_msdos -y /dev/block/mmcblk0p11)
 10. reboot into Android and check if internal SD is writable again

Until now, my internal SD became writable again!
Of course, all data is gone.

Cheers!