Can't watch and download video from iTunes
I had this exact problem with the Stanford iOS 10 course on iTunes for Mac. I eventually gave up and downloaded the videos on iTunes for Windows.

However, I more recently fixed the problem by reinstalling macOS. You can do this by holding Command+R on startup, clicking on "Reinstall macOS" or "Reinstall OS X", and following the prompts.

Note that this will not destroy any of your files or programs. It simply reinstalls the system applications, but any settings, files, or applications that you have on your computer should not be changed.

(You may consider making a backup first.)