Misha came to this school because she wanted to learn how to teach sign language. She's been with Shizune since at least last years festival. After learning sign language, at no point does Hisao ever comment on Misha messing up translations (unless she specifically doesn't know what a word means.)So does Megumeru's urge to over-analyze things.
Is that really what Shizune signs, or is that what Misha translates. Bear in mind, that at this point in time, Hisao doesn't know jack-shit about hand signs, and fully rely on Misha for her to translate anything--if not everything Shizune said. Considering how she usually translates with her own liberties and the lack of 'vigor' Shizune originally have in her messages (top it off with her mistranslation and mispronunciation on some things), it is entirely possible that what Misha said is her own shopped version of what Shizune signed. This led me to believe that Misha learn sign language not too long ago, probably a month or a few weeks before Hisao is admitted--maybe more.
If a friend of her enemy is her enemy, what happens with Hisao starts to warm up to Hanako a bit and suddenly she's a friend of my friend instead?
personally, I don't think Shizune has anything against Hanako personally, she just tells herself that she doesn't like Hanako and uses her to take out some of her frustrations with Lilly.