One great 'ATLA' fanfiction is 'The Avatar's New Adventure' which delves deeper into Aang's training after the series ends. It's full of interesting new bending techniques.
Time travel in these fanfics can completely reshape the Avatar world as we know it from the original series. If Katara travels back in time and alters the waterbending traditions, it could affect how waterbending is perceived and practiced in her own time. Moreover, the overarching theme of the Avatar bringing balance to the world might take on a different meaning. For instance, if a character goes back and changes a key event related to the Avatar cycle, the very concept of the Avatar's role in the world could be redefined.
The 'agni pravesam short story' might be related to the concept of 'agni' which often represents fire in Hinduism. It could be a story that uses the idea of entering the realm of fire (metaphorically) perhaps for purification or transformation. For example, it could be about a person who has to face a difficult trial (symbolized by the fire) and through that experience, they gain wisdom or a new identity. Without more context, it's hard to say exactly what it's about.
I'm sorry, I'm not familiar with the specific 'agni children story'. It could be a story from a particular culture or region that I haven't come across yet.