Ok, first of all be aware that only the Base game and a few Expansion pack will run well on your computer. MacBook Airs are not built for gaming and Sims 3 is a very demanding game that does not work and play well with the kind of laptop you have. Seasons and Pets are right out as they are VERY graphics intensive and may not run at all on your laptop.
So first of all, you're having problems with the installation. Sometimes wireless connections are not very good and while it may be fine for surfing the Internet, downloading games should be done with a direct connection. This means finding an Ethernet cable to directly connect to your wireless router. In simple non computer terms, a cable to connect you to the Wireless box.
Anther suggestions was to go into the setting of Origin. Since it is the Downloads you're having problems with try this. Start up Origin. Look at the menu bar at the top and find Preferences. Check to see if you have set your Downloads (it's about the middle of the page) to "No Limit". If you have not, set both Download options to "No Limit".
Try to download again with a direct connection.
Also after you download the game, Take the time to read this thread as it will help you to install the game on your computer and clear up any additional issues you may have.
https://answers.ea.com/t5/The-Sims-Mac/READ-FIRST-Sims-3-Mac-Help-Guides-and-Troubleshooting/m-p/749664#M3