Assuming you're not in atmosphere and not accelerating, it's just going to hang there.
A flag flaps because of the gases passing it, no atmosphere no flapping. It would however not hang "down" as there is no major source of gravity nearby. The flag would be weakly attracted to the ship's mass and sag towards this mass. However the springiness of the fabric would resist this motion and not drape down like a flag on Earth on a still day.
fly
The part about the spaceship going with the speed of light is not real. I don't understand the earlier part of the question.
This year
Your spaceship.
A spaceship can travel in a vacuum because it produces thrust. The thrust going on the back the the craft actually pushes on the front of the craft (much like a balloon does when you release the untied end. Since it is in a vacuum, there is no friction to slow the craft down once it is moving.
c - Light goes at c in all frames of reference according to Special relativity
Because you're in a spaceship and you're going up.
A space station only has to go fast enough to achieve orbit. A spaceship has to go fast enough to break out of orbit and get where it is going. So, a spaceship.
I'd imagine it would go the speed of light because time would slow down to make sure the light wouldn't go faster than the speed of light.
Discovery
it takes about 3-4 weeks But it Depends on what planet you are going to :)
That will be the Juno space probe due to launch in 2011, reaching Jupiter in 2016.