Delete Origin cache on a different drive
@kittell17 What I meant about transferring the install files was that you could download the game on another computer—a laptop, a friend's system, even one at the library if they let you—then copy the files to a USB, then copy them to your own computer, and let Origin find the files rather than downloading everything. But it sounds like that's a moot point for now, which is great to hear.
For the pack, there are plenty of websites that list them out by release date, so you can see that EP03 is City Living or whatever. I usually just google and jump to the Wikipedia page:
https://en.wikipedia.org/wiki/The_Sims_4#Expansions,_add-ons_and_editions
If you're missing any packs, you can manually start the download through Origin: click on the Sims 4 icon in your game library, select More > Expansion Packs (or Game or Stuff Packs), scroll through the list, and find the one(s) that haven't downloaded. Any you own should have an orange Download button.
As for the household files, I think you're referring to the Tray entries? I sort them by last modified date, so I know what goes with what. But then my Tray folder doesn't have that many files, so it's easier to keep track of everything. You could also copy the files into (properly named) subfolders somewhere else, and copy files from these backups into your main user data folder when you want to use something in-game. But I agree, it's more of a hassle than it needs to be.
