Yes. Snapchat is set up to notify the story creator if you screenshot their story. It's a way for them to have some control over who can save and keep their content.
Snapchat has some measures in place to prevent screen recording in an unauthorized way. It's possible that Snapchat could detect screen recording in some cases, and the user who posted the story might be notified.
Generally, you won't get a direct notification from Snapchat when someone takes a screenshot of your story. But there are no foolproof ways to tell for sure. Some people might mention it to you if they choose to, but that's rare.
To hide a story from someone on Snapchat, you could also create a custom list of friends who can view your stories and exclude the person you want to hide it from. Another option is to set your story to only be visible to your closest friends. It's all about managing those privacy settings to your liking.
One way to watch someone's story again on Snapchat is to look in the 'Memories' section. It might have saved the story you want to see again. Another option is to search for the person's name in the app and see if the story is accessible that way.
The best way to know is to keep an eye on the view count. If it goes up, that indicates someone has read your story. Another clue could be if you get direct messages or comments related to the story from someone.
Yes. Snapchat's system is set up to show the story creator if someone has replayed their story, regardless of the number of replays. So if you keep replaying a really interesting or funny snap story, the owner of that story will likely be aware of it. This feature helps the creators understand which of their stories are more engaging to their audience.