Is there a short cut key(s) that will change highlighted text from upper case to lower case and vicversa?

You can create a shortcut for it in Keyboard System Preferences. Use "Make Upper Case" for the command name and add a shortcut you wish.

I had to play around with the shortcut keys as some combinations may not work. I think you will need command in the shortcut so that the shortcut keys don't delete the selected text. Cmd-ctrl-U didn't work in Safari, here, as it just underlined the text. Cmd-opt-U did work.

Also, if an app has already bound the shortcut you choose, it will do what the app wants, not the Make Upper Case command.

macOS Sierra: Create keyboard shortcuts for apps

In the Mac App Store, get WordService. It is a collection of services that you can apply to text in any application. Among these is an uppercase (All Caps) and lowercase service item.

The act of downloading WordService will install the services, but not activate them. You must visit System Preferences : Keyboard : Shortcuts : Services, and then look for WordService: Lowercase.

Once this service is enabled, you simply select the uppercase text to convert, and from the application menu, choose Services... WordService: Lowercase, or simply the keyboard shortcut associated with it.

WordService will also install an application into your Applications folder, that also appears on the Launchpad. Its sole purpose, when you click its Help button is to open a PDF in Preview describing each of the available services.

Enable only the WordService items that you need.

No key that I know but it is on your contextual menu

There is not a shortcut for it.

But you can create a "service": make a script to do what you want, then with Automator make it into a "Service".

Thanks for mentioning WordService. It has some useful functions. Now if it only worked in Firefox with ASC, which is where I really could use it, I would be a happy man. 😎

Works elsewhere of course.

I noticed that the WordService: Lowercase worked in this reply to you from Firefox 51.0.1.

Hmmm. You're right. I expected "Services" to show up in the drop down contextual menu as it does in most programs. I see now that Mozilla has to be different. lol

Thanks.