When I open a real-time viewer, I see a toolbar with zooming options and a big green box to the far left. What is the purpose of the green box?

Green is a good thing. It means the page was able to subscribe to all its configured tags successfully. You can right-click on the header to hide the toolbar. You can also choose to hide the toolbar by right-clicking the HMI screen in the Realtime viewer’s Custom view list, select the properties item and selecting the Hide toolbar option.