@Demsasha Please run the Origin reset tool for macOS:
https://help.ea.com/en-us/help/origin/origin/how-to-reset-origin-on-mac/
Restart your computer, and download just the base game, no packs. If the download works, great, go ahead and install. If it gets stuck again, then yes, you can install by launching the .dmg. But that only works if the installer is in fact fully downloaded.
Open a Finder window, and click Macintosh HD (or whatever you've renamed your hard disk) in the left panel. If you don't see it, click Finder in the upper left corner of your screen, then Preferences > Sidebar, and check the box next to Hard disks, in the Devices category. Open Macintosh HD, then Library > Application Support > Origin > DownloadCache, and you should see a folder labeled with a string of numbers. Inside should be a ~6 GB .dmg file. Drag that to your desktop and double-click to open it.
To actually install the game, you'll need your CD key. In Origin, open your game library, right-click (or hold down the crtl key and click) on the Sims 3 icon, and select Game Properties. The CD key is the same 20-character product code you'll need to provide the installer when it asks.
Once the base game is installed, please run the Super Patch (digital download version) to manually patch it to 1.67.
https://bluebellflora.com/sims-3-manual-super-patch-for-mac-1-67/
Test the game, and let me know whether you get the unknown error. If you get the server error, that's fine for now—you can fix it by installing almost any pack. But some of the packs need their own workarounds, so please list the ones you'd like to install.
By the way, you can run the Origin reset tool any time it's stuck finalizing or downloading, or doesn't load properly.