br3nd4nt The issue with the installer is that the EA App somehow downloaded the old 32-bit Mac version of Sims 3. The installer is also 32-bit and therefore can't run in your OS. So you'll need to get the 64-bit Mac version into your account.
To that end, please clear the EA App's cache:
https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/
If the Mac version still doesn't appear, you'll need to contact EA customer support and ask for the "entitlements," as they're called, for the 64-bit versions of the base game and any packs you own. You can link this master thread about the issue for the support rep:
Redeemed Sims 3 codes but wont download as says only available on windows? | EA Forums - 11143008
I would strongly recommend live chat rather than email. If you don't see the option, choose a slightly different category of issue.
It should also be noted that it doesn't actually matter where you (or your friend) bought the Sims 3 key, as long as it was correctly registered to your account. Keys either work or they don't.