This is a two-part question, and I only am for sure on the first question.
After you've purchased City Living and DineOut, they should show up in your Origin account ready to download/install. Both may start downloading/installing right after you log into Origin.
However, if they don't. Go to the Games Library and click on the Sims 4. Scroll down past the Play button. You should see a tab called Extra Content. Click that. This will show you what Sims 4 content you have purchased.
Anything that hasn't already downloaded/installed, just click the Download button.