Why does ανοίξεις take that form (instead of ανοίγεις)? Is this like a subjunctive mood?
I'm not good at Grammar, but yes, according to this table: http://moderngreekverbs.com/anoigo.html it is the subjunctive aorist.
To explain it as I understand it, the difference between ανοίξεις and ανοίγεις, is that ανοίξεις refers to an action happening once, and ανοίγεις refers to an action happening continuously or repetitively.
So in this sentence, you will open it once, and "until you open it" is "μέχρι να το ανοίξεις".