On October 8, a boy sent his thirteen-year-old classmate a phone message which he had written in an extremely unclear dialect. So the girl believed it was a threat and somebody wanted to kill her. Consequently, the SMS caused a police operation lasting two days. Finally, the police caught him and put him under arrest. Surprisingly, the police could not do anything against the boy because he - not having intended to threaten her - only had wanted to tell the girl that he had had a dream about her.

Good job, nick.

The date can be written as:
On 8th October
On 8 October
On October 8
All three are possible in Britain, only the last in the US.

Is this a phone (=voice) message or a text message?

I'd suggest:
... resulted in a police operation lasting two days.
... the police could not take action against the boy because he had not intended to threaten her, but had only wanted to tell her about his dream about her.

Meine Anmerkungen:

'On the 8th of October ...

Finally, the police got hold of the boy and put him under arrest.
Surprisingly, the police could not do anything against the boy because he - not having intended to threaten the girl - only had wanted to tell her that he had dreamed of her.' . . .

As SD3 points out, On October 8 was correct. (I always spell it like that, I might say it the way you just wrote it down.)
Why do you want to say get hold of instead of catch ? You normally catch a thief or criminal don't you ? And as the boy is believed to be the latter, I think it is absolutely okay to use catch here.
Swapping the order of the girl-her is a good idea so the relationship gets clearer.
After reading my text again, to have a dream does indeed look strange here, so it is better to say, as you suggest, dreamed of her.

As SD3 points out, On October 8 was correct. As are the other two options I gave. :-)
The last sentence with "- not having intended ... -" sounds French rather than English to me. *g*

But as you said, the other versions would be British.
French people would tell you that it sounds trop anglais :-) (Ils n'aiment pas du tout le gérondif dans ces phrases-là quand il manque d'un "en" ...)
It's just formally overblown *g*

--

goo' nigh' da everyone !

How do you know Susanne doesn't want British? She started with British but just made a couple of small mistakes? I would take that as an indication that she does want British.

What do the French know? But seriously, I think it's better the way I put it - certainly more natural English IMHO.

Sorry, did I miss something? How can anyone tell if the translation is correct without the original German text?

Intuition, Sachs, intuition and decades of professional experience. ;-)

May I come back to you when I'm looking for a clairvoyant the next time ? :-)

Sure! I'll give you a free trial:
May I come back to you the next time I'm looking for a clairvoyant?

Piece of cake! ;-)