1. Is the listing created by a user not claimed by that user automatically?
That depends if the user has ticked the “Business owner/associate” box as YES or NO. YES results in a claimed listing, NO means unclaimed.
2. We need the “Send Enquiry” form to send the copy of the enquiry to an admin’s email address. Is this possible?
GD > Notifications > Site BCC Options > Send enquiry >YES
3. Your best option is to use the Pricing Manager to set different levels for your listings, and then sort them as explained here: https://wpgeodirectory.com/how-to-sort-listings-by-price/
Your site is a combination of HTTP and HTTPS, see WP Settings > General > WordPress Address (URL) and Site Address (URL)
Please fix that first, this may assist:
https://wpgeodirectory.com/docs/useful-plugins/#bsr
Thanks