Can I view the streamed videos full-screen?

Yes you can, with one exception.  That option is available by clicking the 'full screen' icon at the end of each progress bar.  Click on those little arrows on the live stream, screen and on the little rectangle with corner marks on the individual show pages. 

There is always an exception...  The individual page enlarge does not work if you are browsing in Firefox, but does work just fine in Chrome, Safari and Internet Explorer.  If you use Firefox, click on the “Archive.org” symbol.  You can go full screen with the Archive.org version of the video.