If I get the 360 retail copy of this, does it play off the disc or does it install to the hard drive where it is played with the original's disc?

I can't find anything "official", but several forum posts say that yes, it does require the disc.  Since BioWare are calling this an Expansion Pack, which in the old days almost always required the original game disc, I'm inclined to believe those posts.

You can player it right off the disc. It does however require data from Dragon Age: Origins.

It is indeed standalone. I think Arthur Gies on Rebel FM mentioned this. As in you can start Awakening without a save from the original game. I think.