The Planet Express Ship's engine is no ordinary engine. It was made by THE PROFESSOR! The engine is fueled by Dark Matter and was made to move the universe around it.
For all we know, the Planet Express Crew went to the edge of the universe in a week or so but the time frame was just skipped so the episode could continue.
The show sometimes skips travel time to get the plot started, some plots are within the travel time so they don't skip it. This way the show can have a more opened show.
Its like cutting the boring scenes out.
As for the shape of the Universe, I don't think there was anything in Futurama saying that the universe changed. So it would be likely that normal expansion of the universe has occurred.