No. By definition, a private story is private, which means only the creator of the private story has the control over who can view it and the people included in it are not visible to others.
In most cases, people cannot see who is in the private story. Social media platforms that offer private story features usually ensure that the privacy of the content and the participants is maintained. This is to respect the privacy of the users who choose to use this feature. For example, on Snapchat, if someone creates a private story, they select the specific friends who can view it, but other users have no way of knowing who those selected friends are.
Typically, no. Private stories are designed to be exclusive. Only the person who makes the private story can decide who gets to see it. And the identities of those involved in the private story are not disclosed to the general public or other users who are not part of it. It's a way to share more personal or selective content with a chosen few without the worry of others prying into who is included in that sharing.