Finally I have managed to solve the issues with the repo.
The problem was the faulty hdd in my PC. (However it was only 2 months old.)
Because of the hdd I/O problems, my host randomly automatically re-mounted the / file system (including my /home) as read only. As I didn't realize this when I was following the steps in the HADK, when I got a symptom of the wrong hdd, I tried to workaround it. Obviously that has messed up my sfos build environment. Badly.

Anyway, after replacing the hdd I started everything from scratch again.

This time worked the repo init, the download of cm-12.1, everything else!
I let the download run over the night and got some sleep but by the morning my pc downloaded all files.

So, I have completed the 'repo sync --fetch-submodules' step and now am at step "5.3 Configure Mountpoint Information" where I need a little help to understand it. I am not sure whether I need to do something with this step at this point or this is just an information (explanation) for the later steps.
I much appreciated if somebody could help me out with answering to this.

@mautz, Can I ask you to send me your hammerhead.xml from the local_manifest folder, please?
I added that two lines the hadk suggested 'device/lge/hammerhead' and 'kernel/lge/hammerhead' plus added three more 'hybris/droid-hal-version-hammerhead', 'hybris/droid-configs' and the 'rpm' but I am not sure whether this is enough or I need to add something else too. Thanks.