The Germans hired by the Roman state to fight under Roman commanders were very loyal to the Roman Empire and its traditions?

As stated before, yes, the Germans hired by the Roman state were for the most part very loyal. They were used as the emperor's personal bodyguards (and his family's) and some were also hired as lictors who guarded the various officials. Yes, there was the Teutoburg nastiness, but that was instigated by only one German traitor, Arminius, who only had the support of his own tribe and some of their allies. We also hear of the "Germanic" invasion as one of the causes of the fall of the western part of the empire, but these "invaders" were of various tribes all lumped together under the term Germanic. Some of them even settled within the Roman empire with Rome's permission.