In general, no. Snapchat has features that alert the person who posted the story when it's been seen. This is to maintain a level of privacy and awareness for the users.
You can't watch someone's snap story without them knowing. Snapchat has built-in mechanisms to keep track of views and notify the owner of the story. It's part of how the app works to protect users' privacy and give them control over who sees their content.
No, you can't. Snapchat is designed to notify the sender if their story has been viewed.