I don't know the specifics of the German case specifically, but here are some buzzwords to explain:

• let in refugees – basically what it sounds like. There's such thing as too many refugees and for a short while it did overwhelm the authorities (not in like an apocalyptic way, but still a small problem). It's mostly been solved now with tightened checkpoints and the whole thing about that but obviously some people won't be happy until it's completely closed off and everyone is refused.
• tearing the country apart – In Europe immigrants from former colonies and the Middle East are kind of in a bit of trouble as the culture isn't too great at "integrating" new kinds of people. First-generation immigrants can generally keep their stuff together (relatively) but the really big problem is their children who are having a tough time adjusting to being in between two cultures that have a mutual distrust of each other (think the Joy Luck Club style problems but multiplied by a hundred). This leads to a lot of delinquency among them but it's nothing inherent about "Muslim"/"Black"/"African"/etc. that makes them do that and it comes down to needing better integration programs.
• In the same vein, Sharia law is generally blown out of proportion. It's only as psychotic as the people enforcing it, and it generally is only enforced in a community and not something they really care about becoming national laws. Of course there are exceptions in particular fringe cases but in general Sharia Law is on the same level as religious laws for Christians etc and if you allow the Catholic/Lutheran/Protestant Churches to operate then Sharia law is not that different, it just has a foreign-ey name.

In general these are all problems yes, but mostly they are blown out of proportion and need to be addressed by both sides.