I'm not quite sure what the issue is you're having with the second question in the OP. I leave plenty of stuff downloading in the background while I play offline games. So long as you're connected to the internet, the download will continue.
Are you sure you didn't just pause the download or something?
To give you an example of what I mean:
1) Start download of something, say Infamous. Set to background download.
2) Leave the internet connected.
3) Do other stuff, such as play an offline game, like The Sims 3, or a PS1 game.
4) Finish playing Sims 3 or PS1 game after an hour. Turn off console.
5) Turn on console a few hours later. Go do download management, choose Infamous and hit "resume" (It will pause when you switch off the console iirc, but it will keep all the progress it made)
6) Rinse & repeat until the download is finished.
If this isn't what happened for you, then I'd say something must've gone wrong, because it shouldn't reset back to 0% unless you cancelled the download, and it shouldn't pause itself when you're playing another game.