Thanks very much for all your support!
At least I can tell that the battery problem solved itself. It seems that after some charge and discharge cycles the battery meter recalibrates itself back to normal values. It took about 8 cycles charging from dead-as-a-dodo to 100%, but the battery meter is now back to normal again and shows no significant decrease after about 4 days.
It was a sudden change, there was no improvement in usage time. It just went back to normal after charging. And guess what: Its shutting down properly again!
@slvrsplsh: Did you try deleting the file using a root explorer? At first I tried to find it on the READER and SETTINGS drives but its an internal file. Since my device didn't root anymore I had no way to delete the file.
@Harry: Thanks for the tip!
Indeed I was keeping the OS Firmware on the SD card to be able to rescue any time. I will try rooting it without SD card as soon as I picked up some courage again...
...joan