As far as the beginning of Solo's backstory in the EU, I thought they established he was a 10 year old thief who got captured by slavers, but not much more than that, right?
Also, one thing that always seemed odd to me about Han being in the Imperial Academy was how he has seemingly no idea how to handle the radio protocol on the Death Star in Episode IV. "We're all fine, here, now, how are you? *cringe*", boring conversation anyway, etc. I wonder if in this movie, maybe he didn't get far enough to learn that kind of thing? For that matter, I wonder how much they'll tell us about the Imperial Academy. Presumably Tie Fighter pilots come from there after they stopped using clones, and we know that's where Biggs went before he defected, and where Luke wanted to go if not for Uncle Owen constantly putting it off in favor of keeping Luke on the moisture farm. But we never really saw anything about the academy until now, except probably in EU works.
Depends on which story you read and believe to be canon. In the Han Solo trilogy (The Paradise Snare, The Hutt Gambit, Rebel Dawn) he's raised on a smuggler's ship by this man known as Garris Shrike. There was also an aged Wookiee female Han was close to, which sort of explains his affinity for Chewie later I guess?
Han was told he was an orphan and when he later gets away and finds his cousin Thrackan Sal-Solo; they discuss the fact that his parents disappeared mysteriously. (But they're not named.) In fact, doing research at Wookieepedia; their very names are only referenced in one story. (Which I don't remember, but that was eons ago.)
The entire Imperial Academy episode is also glossed over, though Han does sign up under his real name. (This is significant because before this he operated under a variety of aliases.) Then he gets kicked out quickly for interfering in Chewie's mistreatment as a slave. And the rest is history...
Regarding the newer preview, I actually find it less interesting than the shorter one. Hard to say why, though.