Control the publishing of connector

[t-prrath]

Hey all, I have some questions that I want addressed because I have a connector ready to publish but there are some security issues:

1. I can make my own environment but can I publish the connector to that specific environment and add users according to my requirement who only will see the connector to use it in a flow.
2. If the above one is not clear, my question is how can I configure the publishing of my connector so that it is available to use for people I select and I have the choice to make the connector public in future.
3. If I cant publish the connector to my environment, can I share it in my environment so that only those in the environment can see it(cant edit it); just use it in flow.