Displaying Events by category and other criteria

I have 2 categories of events: professional classes and group classes.

I see where I can create a menu item that will display the events by category.

That almost works. How do I get this system to not display classes that are over? While the system doesn’t let people register for a past class, it really should show it.

http://birthjourneys.org/classes/professional/

My next question is, if I use the events archive for displaying my classes how can I show the category as the page title at the top? It’s somewhat ridiculous to not have a title on the page, and ideally a description (which could easily come from the category description)

I see that there is a shortcode to display the event archives, but don’t see any documentation on variables to use with it (assuming there are some). That seems like (if it actually works) it would solve both of these problems.