As to the archive stamp, that would have been put on the document much later after the letter was placed in an archive, not when the letter was being written.
If Miss Jackson, wrote out the words for Alix to trace over, then that would not be a good example of Alix's actual handwriting, just a facsimile of Miss Jackson's.
I would hope, for Anna's sake, that it was genuine, but I had trouble with the way that her elders were addressed as some others here have had.
Personal letter or not, there was a proper way of addressing elders in that era and children did not have any leeway in that. It was proper etiquette and was always observed until the elder gave the child consent to change the way the elder was addressed. Even in my own era, my mother never allowed me to call her friends by their first names until the friends gave me permission. If permission never came, then even as I grew up and became a woman myself, I still addressed them as Mrs. .... or Mr. ..... That's just the way it was.