Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. Some fanfictions might explore Bell's fear in relation to his complex relationship with Hestia, perhaps due to her over - protectiveness or his own insecurities in the face of her expectations.
Well, it's a bit tricky to pinpoint exactly, but it might be in one of the later volumes of the main series. You might have to do some detailed reading to find out for sure.
Their relationship could develop further through shared experiences in the dungeon. For example, if they face a really tough monster together and Bell has to rely on Hestia's support and guidance more than ever. This would strengthen their bond.
There are several common themes. The fear of change is a big one. As Bell progresses in the dungeon and in his relationships, he might be afraid of how it will affect his relationship with Hestia. Also, the theme of facing one's fears in relation to love and friendship. Bell has to confront his fear of Hestia to truly grow and develop their relationship in a more healthy way. Fanfiction often plays with these themes to create engaging and thought - provoking stories.
One plot idea could be Bell and Hestia going on a special quest together that is different from the regular ones in the Danmachi world. Maybe they have to find a lost artifact that has a connection to Hestia's past. Another could be Bell getting into trouble in the dungeon and Hestia having to use her unique powers to save him, which could lead to a deeper emotional bond between them.
I'm not sure specifically what the 'hestia story' is without more context. It could be a fictional story, a personal account related to someone named Hestia, or something else entirely.