Hitler was appointed legally. He was never elected personally, nor did his party ever obtain a majority in the German parliament in free elections. Because of instability during the late 20s and early 30s, the German government was ruled by decree, using emergency powers granted to the President by the Weimar Constitution. Hitler was legally appointed by the President to the position of Chancellor using these emergency powers. He, Hitler, presided over a minority coalition government whose principle political support stemmed from the President himself. However, once he got into power, Hitler quickly outmaneuvered his opponents and legally established the dictatorship. When the President died the following year, the final checks on his own power were removed.

There seems to be a big issue with confusing Hitler's legal assumption of power and whether that assumption of power was democratic or not. It was definitely legal, but never really democratic. We should not mistake the two, however.

Regarding whether the murders of the Holocaust broke German law, that's a thorny issue. Many of the lower level guards being tried today are tried based on Weimar law, which is one of the reasons that getting guilty verdicts has been difficult. It appears that technically, the murders were still murder under Nazi legal codes, but obviously, they wouldn't have been prosecuted if the Nazis had won. And of course, given Hitler's dictatorial powers, there is still a real question whether it was even technically illegal. But this is getting more into the legal thorny issues in the post-war trials and that's beyond my expertise.