No. Private account stories are protected by privacy settings. Only the account owner's approved followers can view the story, and reposting it without consent is unethical and often against the platform's terms of use. For example, on Instagram, if an account is private, the content is restricted to those the user has allowed, and any attempt to repost their story is not allowed.
Typically, you can't view a story on a private account. Privacy settings prevent unauthorized viewing to protect the owner's content and personal space.
Well, as a general rule, it's not possible to see if a private account has a story. Since it's private, the content including stories is restricted to the people the account owner has allowed to follow them. You don't have any visibility into their story status until you become an approved follower.
Definitely not. Reposting from a private account is a big no-no. It goes against the privacy settings and can cause problems for both you and the owner of the account.