[@ineffable] A tiny thing: It still says 'wand core' instead of 'dragon heartstring' in the wand section of the CS. :) And why did Jay go to Durmstrang? You know where Durmstrang is, right? Not in England. While it's not unlikely for UK wizarding families to send their students off to Durmstrang, they mostly do so because Hogwarts has too much of 'yes muggle borns are cool, yes we have a half giant here and love him' kind of policy. 

Edit: Refreshing my knowledge about Durmstrang right now. The school doesn't accept muggle born students. I can't tell if 'half muggle born' is okay, but I doubt it. They seem to don't appreciate muggles so much.

In the quick moment of searching through my information on Durmstrang I couldn't find any information that suggested that the school had a longer education than Hogwarts. So being a student at 19 is very unlikely. Wizards reach the adult age with 17. I can't know for sure that Durmstrang doesn't have 19-year-old students though.