Q. Why doesn't the Zotero window show the items I added earlier this week? Did I lose them?

No, you didn't lose them. The Zotero window that you see in Firefox will show only the items saved to that computer. Since you are working on one of the Libraries' public computers which clear out all personal files once you log off, your previous work won't be displayed.

You can add new items and they will show up in the Zotero window, just be sure to sync your work before you log off or you will lose anything newly added.