Aang might go into a deep state of depression. He has always been an emotional character, and having his heart broken by Katara, someone he loves deeply, could send him into a downward spiral. He might isolate himself from his friends and stop practicing his bending for a while.
Katara could be heartbroken. She might initially be in denial, not believing that Aang has actually left. Then she could become angry, feeling betrayed by Aang's sudden departure.
The Fire Nation, which has now become more of an ally, would also see this as a positive thing. Zuko, being Aang's friend, would be happy for them. He would see it as a sign of peace and unity among the different nations. The Fire Nation people might send some precious gifts as a sign of their respect for the union, as they know how important the Avatar and Katara are to the new world order.
Toph would be blunt about it. She might tell both Aang and Katara that they're being stupid if she thinks the break - up is over something silly. But if it's a more serious issue, she'd support them in her own way. She might offer a place for Katara to stay if she needs to get away from Aang, or she might give Aang some tough - love advice on how to handle the situation.
Katara would likely be shocked and initially angry. She has feelings for Aang and would be hurt by this unexpected turn of events. Zuko, on the other hand, might be conflicted. He wants his sister to be better but this situation is so out of the ordinary. Toph would probably be more straightforward and say what she thinks, which could be a mix of disbelief and amusement.
Sokka would probably be overprotective. He's always been protective of Katara, and now with her being pregnant, he would be constantly worried about her safety and the well - being of the baby. He might offer all kinds of advice, some of which might be a bit silly but well - intentioned.
Yes, if the title 'aang is a firebender fanfic' is to be taken literally, then aang is likely a firebender within this fanfic. However, without actually reading the fanfic, there could be some sort of plot twist or alternative interpretation that might make it not so straightforward.
He could meet his future self. It would be an interesting encounter as he could learn from his future experiences and wisdom. Or he might meet people who have studied his past adventures and see himself through their eyes.
Possibly they are random villagers who were caught in the crossfire of a conflict between different bending factions. Aang, being the Avatar and a symbol of peace, feels responsible for burying them and ensuring their spirits are at peace.