1.) Backing up your game is really simple. Just go to Documents > EA Games > And copy the file called The Sims 2. Then, create a new file in the main list of documents (Or a subfolder for backups) and paste the Sims 2 file there. It's really that easy. And EP Manuals explain it way better than me.
2.) Bodyshop comes with the base game, and allows us simmers to create CC (Or Custom Content) for our sims to wear much easier. It also allows the simmer to create a sims, clone it, or import it into the game or the TS2 website. And no, it won't mess up your game.
Hope that helps!