In most cases, people cannot see that you have blocked them from your stories. Social media is designed in such a way that it respects your privacy when it comes to such actions. Let's say you are using Snapchat. If you block someone from your story, they will simply not be able to view it. There is no message or indication sent to them that says 'you have been blocked from this person's story'. This is to ensure that users can freely manage their audience for their stories without the fear of causing conflict or having to deal with unwanted reactions from those who are blocked.
No. When you block someone from seeing your stories, they generally won't be notified or be able to tell directly that it was you who blocked them from seeing your stories. Social media platforms usually keep this action private to protect your privacy.