Once a game is purchased, you should be able to download it anytime you want. However, to be safe, I would go ahead and download it right away, if you haven't already.
As for backing up the games, there is a thread here on
backing up and restoring Origin games. This works for most Origin games, but it focused on The Sims 3 and its expansions.
Also, if you buy the disc version of any Sims 3 game/expansion/stuff pack, you can register the game on TheSims3.com site and it will also show up in your Origin application. If you haven't installed the disc, you can download a digital copy for free. If you have already installed it, simply uninstall and then you can download it from Origin. I get Sims 3 this way so I have a disc and a digital backup of all my Sims stuff.
If you have any problems registering the game through the site, or downloading from Origin, contact EA support. Despite their bad online reputation, they've always been helpful in getting my problems resolved.
Hope this helps.
Flynn