Motorball takes place in the entirety of volume 3 of the manga (the old release, new release is 5 volumes so I'm not sure which volume its in) and her Berserker body (I don't know if they call it that in the movie, not even close to the power of her current body) is in the manga as well (first volume). From what I've heard it's a pretty accurate adaptation of the OVA which was a haphazard adaptation of the first volume of the manga (still good, I enjoyed it for what it was) with elements of the manga thrown in (badly by what I hear, sounds like the skip all of the motorball stuff after the tryouts which is a bummer since that's by far one of the high points of the manga for me).
Not entirely sure what they said her age was (221 in the manga currently) or what her background is as it's never really covered until toward the end of the manga and the Last Order continuation (to sum it up a Martian terrorist and Panzer Kunst specialist (cyborg martial arts) who was stranded on Earth during the Terraforming Wars on a botched up mission) but I'll have to wait and see as I won't see it in theaters (I'll wait until it hits home video). As much love as I hear for this adaptation I'm skeptical it's any good (I'm a purist who loves this manga and we all remember how much I tore down the GitS movie) but I'm glad you enjoyed it.
Sigh, they just want to adapt everything now don't they. Didn't they learn their mistake with G-Saviour. Gundam isn't meant to be adapted into live-action >.<