Note that this list is not comprehensive. I picked out a few examples of each kind of error or problem I found. Of course, not everything is a black-and-white issue; this is not a list of things you have to fix, but take each under advisement.
First off, I'll say that more mistakes are allowable in this type of format. A narrator shouldn't be misspelling words, for instance, but these are transcriptions of something a child has written, so it would understandably have some mistakes in it. I'll point out what I consider excessive, but it's certainly fine to leave some amount of these in to make it seem realistic, depending on your vision of her intellect and the care she took in writing.
Now to the review. Right off the bat, I'm put off by the use of italics. They're for making things stand out, which means there's a point where they become counterproductive. If everything stands out, then nothing does. They also get irritating to read in large amounts, like reading a story in all caps would be. For this reason, it's fine to put a letter in italics if it's reasonably short and an aberration from the bulk of the narration. Here, the letters are the entirety of the narration, so you don't need the italics to identify them as letters. The format already does that.
Why is this capitalized?
I realize it's acceptable to go without indenting the first paragraph of a story, but when there's another reson for doing so, like holding to the letter format, you should. Likewise, leave a blank line after the salutations. It makes them easier to read. Same deal with the closings, once you start using them.