Hi Isaac,
Thanks for the interest in our plugins, I can help answer your questions.
Events Calendar Pro and WooCommerce Tickets Work Together and can be used together. Each plugin brings in it’s own features.
I’d like to create events that can be browsed with the map view, but I want to sell access to them with the WC Tickets plugin.
This is certainly a possibility. The tickets appear on the single view of the events so they can be shown in any of the Pro Views (Map, Photo, etc)
If the event expires, does the listing in EC Pro and the WC product automatically become inactive?
Yes once the event has past the tickets are no longer for sale, but with each ticket you can set a sale period so you can end it before the event actually starts if you like.
New User Primers:
https://theeventscalendar.com/support/documentation/events-calendar-pro-new-user-primer/
https://theeventscalendar.com/support/documentation/wootickets-new-user-primer/
Those two will show you all the features for each plugin.
And here is our demo with with different views and a single event with WooCommerce Tickets:(in the header menu under demo)
http://wpshindig.com/events/
Does that answer your question?