The only reason why the captcha text can not renew during page refreshing, it’s some cache issue at the website or some php error.
Relative first issue you need to check my previous replies. Also if you submit the booking (if you can submit) do you see the dates as booked after you reload the page?
If there some error, then please recheck your error.log in your server configuration, about any relative errors. If you can not find error.log file, please contact support of your hosting company about helping in finding this file.
Relative questions about the paid versions, please contact here support @ wpbookingcalendar.com (because this forum is only about support of Booking Calendar Free version).
PS Paid versions of plugin does not have trials.