Unfortunately, it has no English subtitles, but the following German journalistic TV program "Panorama" is very informative:
The first segment is about those false reports, how and why they spread, and what's behind them. There're interviews with the police in one case where they "covered it up" for a few days, where he explains that had nothing to do with the accused being refugees, but with the accused as well as the victims being underage. The protection of the victim is totally ignored by the right-wing propaganda.
It doesn't help that Rainer Wendt from the German police union is repeating this rumor about the police having to cover up crimes committed by refugees under pressure of left-leaning politicians. The journalists in that program asked for an example to prove his allegation, but he could not give one.
The second segment should be very interesting to you,
@{ Emilia } , as it shows exactly what you mentioned, the rise of right-wing crime, not only against foreigners, but against politicians as well. It focuses on the experiences of the mayor of a German city where a new refugee camp is to be opened. From death threats per mail to rocks through her window and a group of people standing in front of her house proclaiming loudly they knew where she lived.
Let's not forget what happened in Cologne last October, just prior to the election of for mayor, when a candidate was attacked and injured by a right-wing nut.
Of course, the attacks against refugees is to be mentioned, as well. Recently, an unknown person threw a hand grenade into a refugee camp in Villingen-Schwenningen in the Black Forest. Luckily, the grenade didn't go off, but it shows just how far some people are going with this.
The third segment shows what the pressure of the European Union on Greece to better secure their borders against refugees costs. A NGO committed to save refugees from drowning by meeting them just before the shores of Lesbos and leading them safely on land, helping them avoid the spikey rocks near the shore, has been banned from patrolling the shore. Members of a different NGO with the same strategy have even been arrested and accused of smuggling people across the border, even though they never leave Greek waters.