EU countries would be wise to set a zero tolerance policy and ship the shitheads back.
With many European countries having a conviction rate of below 5%, that won't do. What will be a lot more effective is not to combine different goals.
Germany has a very low birth rate, and Merkel thinks having refugees will stop population decline. This is true, but causes more problems than it solves as they don't bring in the kind of people they need. The surge in crime and unemployment costs will sway the populace against refugees. It also attracts many immigrants from peaceful countries.
All this makes helping refugees from war more difficult.
The solution is to accept refugees from war, while making it completely clear that non of them will ever be allowed to stay in Germany when the war is over. In the meantime do not mix them with the general population but instead build migrant cities where they have to stay during their shelter, while providing them with food, shelter, medicine and other basics where needed.
People who misbehave during their stay there and pray on fellow refugees need to be deported or locked up for the remainder of the war in Syria.
Population decline can be prevented by domestic measures and by allowing migration of people who can contribute, for example educated people from Asia and South America.