Probably. The Arkham series has a connected storyline, and it would make sense for the Arkham Knight new story to be a continuation. This way, it can keep the lore consistent and develop the characters further. For example, we might see how Batman has changed since the last encounter with his foes.
Yes, there are many Arkham Knight fanfics that are suitable for general audiences. You can find them on various fanfic websites by using filters or search terms like 'family - friendly Arkham Knight fanfic' or 'PG Arkham Knight fanfic'.
The Arkham Knight story is of a considerable length. It can take quite a few hours to complete, depending on your playstyle and how much you explore the game's side quests and extras.
Well, the Arkham Knight Bane is a complex character. When paired with an OC in fanfiction, it gives writers a chance to explore different aspects of his personality. Maybe the OC is someone who tries to reform Bane, or perhaps they have a shared past that is only revealed through the fanfic. The fanfiction can also play with the power dynamics between them. If the OC is a weaker character, how does Bane react? Does he show mercy or is he as ruthless as in the game?