The movie starts out with two astronauts playing catch with an egg shaped rock on the moon. Then they take the object onto their space ship, and the crew end up dying from lack of oxygen. The spaceship ends up at a space station, which blows up, a few of the space station personnel escape onto the same spaceship, which has the undiscovered alien on it, some of the personnel get killed, the survivors end up becoming close friends with the alien, who learns our language.
It was low budget, which I'm assuming is why you thought it was an independant film. It has the plot points you described, including an alien who kills almost everyone on board but was only doing so to defend itself. He ends up befriending the two survivors at the end. Below is the trailer.