If you take that Luke was supposed to be 19 in Episode IV and he was born at the end of Episode III, there was a 19 year span to do stuff in. The beginning of the game had the apprentice at like around 5, this would have been around a year into the empire. Biggs Darklight was recruited into the rebel forces when Luke was 18. The rebellion was known about by that time so I am going to estimate that it had been around for about a year. This means 17 years has passed, putting the apprentice at around 22 years old which is about how he looks in the game.
I'm guessing the black lightsaber is 2x bigger then the regular ones?
Nah, But its a beam of light that is black.