Sometimes you can. Like on some messaging apps, you can choose who gets to view the stories you share. However, not all platforms provide this functionality uniformly.
Yes, you can. In Instagram, when you are about to post a story, there is an option to select the audience. You can exclude certain people from seeing the story by customizing the audience list.
Maybe. It all comes down to the functionality and configuration of the platform. Usually, there should be some way to manage and control the visibility of specific stories, but you'll have to explore the settings to find out for sure.