The lore in this world is very interesting, in that the elemental magic is tied to specific "sources" located in Alterdam. I also liked the mention of war here and there, it shows that eventually these chapters will be leading up to something important. I also would like to know why Lea's eyes are golden even though she is a blue and can control water, and I expect that will be a major plot point.
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For the most part, SPaG (spelling, grammar & punctuation) seems of good quality aside from the odd typo here and there (which happen to us all) and the odd tense switch. An example of this is: "she'll be left alone in this place" which should be "she would be left alone in this place" (will - present future, would - past future -- if that makes sense?) Another was "she had recently got those bangs after she got the envelope and elixir." I would instead recommend: "she had recently gotten these bangs after getting the envelope and elixir". Another thing with punctuation is to just watch with the fullstops at the end of dialogue. I think it was in chapter 2 where a list of names is read out. They should be punctuated like this: "Aliah Bell." There are other instances where some fullstops are missing, too.
The Hogwarts references made me chuckle. One thing I was wondering is if going to Alterdam us as simple as closing her eyes and picking it, how come she never tried to go there beforehand? Especially because she was dying to as a kid?
Overall this is a solid start to a story and I'm sure you have lots of things up your sleeve in regards to the war and her golden eyes :)