No. Generally, a private post is private for a reason. It's not designed to be shared widely like on a story. A private post often has restricted access for a select group or just the user, and sharing it to a story, which is usually more public - facing or at least accessible to a wider audience, goes against the concept of privacy.
You can post anything that you want to keep private but still want to document for yourself. It could be your innermost fears, funny incidents that happened only to you, or your secret aspirations. Just make sure it's something you're comfortable having in a private space.
Sometimes, the app might be having temporary issues. Wait for a while and try again later. Also, make sure you're following the app's posting guidelines and that your content doesn't violate any rules.
Yes, usually you can share your post to your story. Most social media platforms have this functionality. However, it may depend on the privacy settings of your post and the specific rules of the platform.
In many cases, yes. However, make sure the post is publicly available and that the platform you're on supports sharing to stories. Also, check if there are any specific conditions or limitations set by the owner of the post.