Is there a way to know which Pivotal Cloud Foundry licensed version we are using?
I see there are some marketplace services offered free in Public PCF b
When you mention "Public PCF" I assume you're referring to Pivotal Web Services (https://run.pivotal.io/)? PWS is configured with access to a public marketplace with partner-supplied tiles / services. The private PCF that you're using is administered by your operations team, and it is basically up to them to decide what services to install / make available to you. You can find the list of available services for private PCF installations on the Pivotal Network site here: https://network.pivotal.io/
If you see the service that you need listed there, chances are that your operator will be able to install it onto your private PCF