Hi
Try launching the game from the base game icon in Applications/TheSims3 folder, instead of from Origin.
To download Store items these days you need to have the Launcher open before you click download on the item in the Store or your Purchase History. Get the Launcher open, set it to the Downloads tab and then start clicking things in the Store. I just do a few things at a time. It may take quite a while between clicking to download and the items actually starting to appear in the Launcher, especially the first few.
Also ensure you are patched up to date, as some Store content requires later patch levels.
For general advice, information and tips on how to play TS3 on a Mac, read BluebellFlora's guide here:
http://answers.ea.com/t5/The-Sims-3/Links-to-Mac-help-threads-and-guides/m-p/749664#U749664
Caspin
