Yes, we outran the light coming from the galaxy earlier on as the expansion was quicker then and we were carried along with it.
No, it doesn't violate Relativity since our coordinate speed with respect to space locally was always zero. It wasn't us moving, it was the space between us and them that was expanding.

Oh and Einstein's earlier work is all about the implications of light always moving at the speed of light regardless of the speed of the observer.