I can't answer the second question, so I'll just stick to the first one:

Indeed, there are many accounts of Vikings in Germany. Especially the rich Rhineland was raided repeatedly in the 9th century. Most notable probably were the raids of the "Great Heathen Army". After being forced out of England, they turned to plundering the Low Countries and in 881 sailed up the Rhine.

Cologne, Bonn, Neuss, Jülich and Andernach were plundered or forced to pay large amounts of "Danegeld" (bribes) - and in the case of Cologne, the city paid when the Vikings sailed up the Rhine, but couldn't pay another time when they returned and subsequently the city was torched. The city walls remained blackened by the fire until they were razed in modern times.

In the Rhineland, the Vikings encountered the old Roman street network and used it to expand the area of their raids. Subsequently, they plundered Aachen - and even the cathedral where Charlemagne was interred.

After Aachen was sacked, they plundered in the Eifel region. The rich monastery of Prüm was sacked before the army turned to the Moselle area. There, when marching on Metz, they were finally met by an army of the archbishop of Trier and the count and bishop of Metz. Even though the Vikings won the engagement, they turned around and left the area, most likely fearing more resistance.

Meanwhile, the Frankish emperor Charles III ("the fat") had returned from Italy, where he had went in 881 to get himself crowned emperor. He held a Reichstag in 882, gathered an army and moved towards the fortified camp of the Viking army. But it did not come to a battle, but rather the Vikings paid a "ransom" and left the area.

While this is only one of many raids, it is probably the most notable and should serve as an example to answer your question: Yes, the Vikings did indeed raid into modern Germany.

/u/Kartoffelplotz points out the major raid in the later 9th century but I thought I'd chime in just to note the sources where you can find these accounts and also to give a reason why you might not be familiar with raids there.

Out best source for Raids up the Rhine and into Germany come from the major annalistic source The Annals of Fulda which you can actually read in translation by Timothy Reuter. Hints at raids like these also appear in Regino of Prüm's Chronicle and in The Annals of Saint-Bertin both of which are also available in translation.

The reason why you may not have heard of German raids is two-fold. Firstly, there were indeed fewer of them and really when we look for concern about outside raids and invasions our eastern-Frankish sources are much more concerned with Magyars and Slavs than with Scandinavians. This has a lot to do with geography and politics which leads to the second point. Unlike Western Francia (i.e. France) East Francia (the roots of Germany) shares a border with Scandinavia and thus the possibilities for direct political engagement with Scandinavian leaders was higher. In East Francia we often hear about a Viking attack followed by an apology from a Danish king or an outraged envoy from the East Frankish ruler. In West Francia and England on the other hand, raiding was far more active but also far more transgressive and unexpected, with none of the trappings of political interaction, at least at first blow. West Francia, the Netherlands, and the British Isles were all much easier targets and were more readily available to Vikings who might be leaving Scandinavia for a reason and didn't want to get caught up in Danish or Swedish politics.

As for your second question, we know that several attempts were made by Scandinavian leaders to rule on the continent, always interestingly enough, within the context of the Frankish kingdoms. Unlike in England, Ireland, or the Scottish isles we don't see Vikings attempting to carve out their own territory on the continent (though the Viking kingdom in Brittany in the early 10th century might be an exception). So in that context the Vikings seem to have viewed their "conquests" as somewhat familiar areas, a system they wanted to join for its wealth and prestige (the fact that they often are baptized and marry important local women is equally telling) rather than something to be stamped down.

I'm not an expert on the Danelaw or the Hebrides etc. so I'll leave that to someone else, but on the whole my hunch is that there was generally more that was similar about these various North Sea/Atlantic peoples than dissimilar (religion not withstanding).