Transportation signifies a sort of freedom typically American, and even by the 1920s the car was a symbol of American success. Transportation can be vertical as well as horizontal. As for the former, we see people such as Gatsby reaching up to the pinnacle of the American Dream, trying to "travel" to that place by false, unauthentic means, and as for the latter, we see Nick traveling East in search of his American Dream even while the eariler myth in American was to "travel west" to seek fortune, opportunity, and freedom of space.
Tricky question. I think the most important role belongs to Gatsby's car. His car is used as the vehicle (pun intended!) for creating the last conflict of the story. We've been shown this dirty, dingy, gray road where nothing lively or exciting happens between the Eggs and the City. It's been presented simply as a road that's there and traveled upon. Only the appearance of Myrtle breaks the monotony of this well traveled road. Then, without warning, the single incident that leads to the end of every character occurs along this very road.
Fitzgerald certainly does a nice job setting us up for it, though. Throughout the novel we see various modes of travel that are simply used as travel. We don't expect the car ride home to be the horrible conflict; we expected the conversation that would be had once everyone reached home to be the conflict.