I've never worked on AoS, so I can only speak from having worked on other GBA games.
1. I would imagine that every game is specific on where the dialogue is located and how it is stored. How difficult would it be to locate the starting and ending points of the dialogue and extract it?
As you said, every game is different. Some games can take a few minutes and other weeks or even many months to extract it correctly.
2. Assuming I can even locate it and dump it, I know I only have a limited amount of space available to change the script.
This is mostly incorrect in my experience with the GBA. It's extremely easy to expand a ROM and add a ton of free space, so you shouldn't have to worry about that.
Of course, you need to know about how to work with pointers, at the very least. If the text in the game is hard-coded or inside a custom scripting engine, you may need to be good with ASM too.
(By the way, you should read the "Personal Projects' Additional Rules" sticky in this forum, as this thread should have been posted better in ROM Hacking Discussion, I believe.)