Alright so, I've never seen this series, so I know nothing about it. I didn't even see the movie when it came out (and continued not to see it, because I was told it was horrible). I'll do my best with this comment though, basing it off of writing ability rather than storyline or anything like that.
Summary: I can tell from the summary, that you have put a lot of thought into this. It's something you obviously really like, because you've got it all worked out. However, I do have a few issues with it. First off, is it common in that show for people to be able to master more than one of the skills? And the part about her grandmother, and it meaning that she is great at meditation and very calm. It all seems to make it sound a bit Mary-Sueish. I'm not trying to knock your story or anything. I just know how easy it can be to fall into that pit where you try to make everything easier for yourself, or try to do everything you've always wanted to do with a character.
Still, I could be wrong, so ignore if you think I'm wrong.
Chapter One: I think there's a lot of things that you explained through narrative with this, that could've been implied. Like, with the tea shop, instead of saying that she's their best customer and they like her there, you could've written up a small banter between her and the worker, or when she came in, they know her order already. I know when I go into most coffee shops around where I live, I get big smiles and waves, because I'm there so often, and if I order something that I don't usually, people get confused. It's all about realism with writing. You have to make it appear like real life, even if monkeys are falling from the sky, and the ground is made of fire.
I don't have time to read the rest really, as I gotta get off the computer and get my own stuff done. However, as I said, you seem very devoted to this story. That much is obvious through your detail. To improve upon it though, I would challenge you to try stepping more toward implying detail rather than flat out explaining it. The same with the summary. You give away the first half of the story, so people don't really need to read it anymore. Give them just enough to hook them, and then leave them hanging so that they need to read it to find out more.
If you ever need help with editing, or if any of this comment is unclear, I'm totally open for editing. I love to edit, and I love to teach. I would be more than happy to walk you through things that I had to learn along the way as well. I've been at this writing game since I was in elementary school, so chances are, if there's some unknown grammatical rule you're having trouble with, I've researched it in full.
Loved the chapter. I have no idea what she is going to do about Zuko. But because you are writing this I know it is going to be good. Keep it up katie. Update soon?
I love the story! though I am finding it difficult toread the dark text with the background, which is a cool background by the way. I can't wait for the next chapter.