Nezuko is initially 12 years old in the manga. As the story unfolds, her age doesn't change significantly in a traditional sense, but her character development is quite remarkable.
The term 'STORY' doesn't really have a widely recognized 'full form' in the sense of an acronym. However, if we were to be creative, we could say 'Sequence of Telling Our Real Yarns'. But in general usage, 'story' is just a basic English word referring to a narrative.
A simple Nezuko and Zenitsu fanfiction could be that they go on a journey together. Along the way, they encounter other demon slayers who are initially skeptical of Nezuko. But Zenitsu stands up for her, explaining that she's different. This shows the depth of their friendship and how Zenitsu has come to trust Nezuko completely.