Thank you for the actual statistics; can you provide a source for the legislative change? I found sources for 2005 and 2008 changes, but not one for 2013.
There's also one particular thing that doesn't pass the smell test for me from your German article:
"Less than 1 percent of the total crimes committed by refugees are sex crimes, going against rumours spread on social media that these have become more common with the arrival of hundreds of thousands of refugees."
1% doesn't strike me as a very low percentage of sex crimes, but I googled around for some statistics, and found another article from the same source - https://www.thelocal.de/20160218/refugees-to-germany-commit-...
Here, the title is that "refugees commit less crime than Germans". However, the stats they quote show otherwise - despite refugees being anywhere from 0.8 to 2%, they committed at least 4% of the sex crimes in the country - a factor of at least 2. The article itself says that the sexual assaults reported during the New Year's Eve were not part of this number, so this is a conservative estimate. The article quotes a ratio of 2:1 men over women as a mitigating factor, however, doing the math most favorably towards refugees(100% of sexual assaults committed by men, 40/60 split in men/women in Germany) leaves you with an adjusted rate of ~2.6% of crimes, still significantly higher than their proportionate population.
From that article though I was able to acquire this statistic for 2015:
"The total number of this type of crime committed nationwide throughout 2015 was almost 47,000"
From here - https://www.osac.gov/pages/ContentReportDetails.aspx?cid=170... - I found that the total criminal offenses in germany were close to ~6mil. From this you can calculate the rate of sexual assault for the german population - 47k / 6mil ~ 0.8%. It's not as significantly different from the previous number, but still doesn't support the claim that, at 1%, refugees commit less sexual crimes than the german population.
EDIT: There is also a mitigating factor I just thought of that the newspaper didn't mention; refugees are likely to have a poor economic status in Germany, and are thus more likely to commit crimes for that factor alone. I don't know how to calculate for that as well.