Any movement in space is time travel to some degree
However, we think we know what the limits are where we are, but there are lots of places in the universe where these "commonly" known laws don't apply. Think of a black hole. Does light move faster there or not. We do not know and cannot know until we do practical experiments. Some say that we would stretch out like spaghetti if we entered a black hole. But since black holes have a larger event horizon than a point, we may well survive the travel. After all, we are almost 100% empty space. Gravity is different than the boost of a rocket, because the rocket pushes You through a surface, Your skin on Your bottom (if You are sitting), but gravity pulls You at every point in Your body at the same time.
As for breaking the laws of causality; if something gets changed then it was always that way, no matter how many times we change it.
