Is there something special to do in order to get the option to see a map of 'Where we Live'?
I saw a site created with CC and there was the option to Show Classmates on Map, but I don't get that on my site. Is it dependent on the theme used to build the site?

Go to Edit Pages and click on Home Page. The "Where We Live" option is there, you just need to click to activate it

Is there a way to display this map only behind the log in? This is a huge amount of private information to be displaying publicly.

Yes, you could take the code and put it on a separate page that is PRIVATE. Use "View Source" in a browsers to copy and paste the code. Search for "Where We Live"

Here's a page I quickly made for OUR site, Could make it prettier.