Such a great story! You give Binns such a perfect voice, and you truly make us see how his mind works. Things are so eminently logical from his perspective, and on those occasions where other people are completely unlogical, one sees how strange and confusing this is.
It's a marvellous depiction, and Walburga, or the little we see of her from Binn's POV, is very believable, too. One sees what she gets from the friendship.
Binn's contacts with his colleagues are just so. I can see Filius's tactful friendship in drawing the diagrams, and presenting them as an interesting problem for two Ravenclaws.