According to that wikipedia article, the German law translates Volksverhetzung into English as "incitement to hatred". So no, saying that Germany has banned 'hate speech' is not an oversimplification chosen by the media. You are intentionally conflating politically incorrect opinions about immigration (aka 'hate speech') with child porn and violent threats.
Volksverhetzung is very precisely defined by decades of legal precedent and much narrower than what an English speaker would think of when hearing "hate speech". Just because translations made for the convenience of non-German speakers chose a specific translation doesn't mean that it captures the meaning with all attached connotations well.
Two examples (without saying anything about the validity of the claim): "Recent immigrations are responsible for violent crime including rape. To protect our people we need to reform our immigration policy" – absolutely fine. "Gang-raping immigrants are roaming our streets. We need to wipe them out before it's too late" is not. You are not helping political discourse with the latter either.
No, even with the second sentence it is still borderline. According to regular case law of the Federal Constitutional Court the most charitable interpretation needs to be taken. Without the second sentence this is a factual statement (even though extremely worded, it has happened at least once on New Year's Eve 2016) and transports a political statement. No court would do anything about that.
Twitter has nonetheless removed a very similarly worded tweet by a member of parliament.
> No, even with the second sentence it is still borderline.
I'm afraid I don't understand what you mean. In your previous post, you said the two sentences were not fine (i.e. they did qualify as Volksverhetzung). But now I understand you're saying the opposite? Or did you want to say "... even without..."?
> Twitter has nonetheless removed a very similarly worded tweet by a member of parliament.
This is what I was getting at; for anyone else reading, an AfD parliamentarian is under investigation after 100 odd denunciations for a tweet very similar to the first sentence, i.e. she said something like "Gang-raping immigrants are roaming our streets". She did not -- at least as far as I'm aware -- call for any violence towards, instead, she was opposed to official tweets from the police being communicated in Arabic.
I am not comfortable giving a assessment of the second example with both sentences. Rulings might turn out either way depending on context and I'd advise not to publish anything close to that. It starts going into Volksverhetzung territory.
She tweeted something like the second example, first sentence only. There should be no legal problem with that (it was just a pretty extreme wording of "the police shouldn't tweet in Arabic"). Sorry if I didn't make that clear enough.