While we do not have any admin demos at this time, you can see a demo of the front-end functionality of The Events Calendar and its premium add-ons at wpshindig.com.
If you would like to see other examples of the plugin "in the wild," i.e. out in the real world, then check out some awesome examples of sites using our plugins in the Showcase.
While we do not have an official "trial license" or "trial period", we do have a thirty-day, no-questions-asked refund policy that many folks use to facilitate a "trial period."
This refund policy, which you can read about here, lets you tinker with the premium add-ons for up to thirty days; if you're not satisfied, simply head to this page and request a refund. We process refunds in usually no more than a few more hours.
If you have any questions about the functionality of features of our various plugins, head on over to our help desk.