I really enjoyed this. I've seen second person overused in fanfic but it works absolutely perfectly here for what you intended, a kind of meditation of the often wordless interaction between a student and teacher at times. I like that bit about Snape hardly ever leaving a comment and that probably being indirect praise. That sounds very much like him.

Unusual, measured and thought-provoking take on the situation. I like the way you have maintained the anonymity of the protagonist, even to the point of keeping the gender ambiguous. The attitudes expressed towards learning and the value of knowledge make him/her sound like either one of the more intelligent Slytherins or a Ravenclaw. Can't see Hufflepuffs wandering forbidden coridors, or Gryffindors sensibly agreeing to destroy the letter. It's touching that Snape had his own 'foolish hope' - that someone would continue to have faith in him.

Sounds like a Ravenclaw. A satisfying read.