Hey @Alan,
Thanks for reaching out. If the shortcode is just staying as the text of the shortcode, and not rendering as it’s supposed to, then unfortunately your theme or another plugin is breaking the shortcode functionality on your site. If you’re interested in finding out the source of that problem, you can run through the complete set of troubleshooting steps on this page and check on the shortcode issue after EACH step in the process → https://theeventscalendar.com/knowledgebase/testing-for-conflicts/
Now, as for the general question of how to show upcoming events on a mobile view, by default The Events Calendar and its add-ons are fully responsive. They have their own mobile display.
You can see these various mobile styles in action on our demo site here → http://wpshindig.com/events. Check out this page on a mobile device and navigate around to see the various styles.
If you want any other mobile styles than what you see on that site, then unfortunately you would have to custom-build those styles on your own (or hire a professional developer to make those customizations for you).
I hope this information helps! Let me know the result of your troubleshooting step testing and if there are any other questions I might be able to help with here.
Cheers,
George