Chances are, no one will know if you screenshot their Facebook story. Facebook doesn't have a direct way of alerting the owner. However, it's always good to respect others' privacy and use this option sparingly.
In most cases, no. Facebook doesn't have a built-in feature to notify the person if you take a screenshot of their story.
Usually, someone can't tell if you screenshot their FB story. But keep in mind that some third-party apps might claim to offer such detection, but their reliability is often questionable.