Hi Paul!
Thanks for getting in touch with us! Let me help you with those questions.
1) I could not reproduce this issue using the storefront theme in my own local installation. Could you please share a link to your site so we can see if we can find the problem?
2) If you want to make an event private, you can do so by changing its visibility setting. See here > https://cloudup.com/cyca52VBy8q
3) I can see from the screenshot that some of the texts are cut off. So please share a link to the site so I can have a closer inspection and find the conflict.
4) Could you please specify which label names you want to customize? We have an extension to Change the Labels for “Events”, “Organizers”, or “Venues” > https://theeventscalendar.com/extensions/change-labels-events-venues-organizers/ Does it help with what you are trying to accomplish?
Please let us know.
Best,
Victor