Wow, quite a bit going on here. Since we're sharing, here's my hypothesis at this point:
This Black Class was convened as a method of "pushing Tokaku out of the nest", so to speak. Consider that she's an assassin who has never killed. Why? It can't just be that it's school; the others already have their first kills under their collective belts. But the characters we've met also have another common point: they have a reason. They have...let's call it a Focus. Capitalised; official like.
I would put forth that Tokaku doesn't, and this whole game is to engineer that. Be it from a strong protective impulse or desire for revenge in the event she fails to protect Haru or something else entirely, the intent is that she come out of this with the a Focus so she can do her job. We've been given some indication that she's previously been driven by her family situation, but my read of that scene is it's not important enough to be her Focus. Considering she was unable to kill Isuke, I think this is a fair assessment.
Also recall that Kaiba implied she was monstrously deficient from the very start, and it should be clear that he's attempting to manipulate her development via his riddles. There's no way he doesn't know what's going on, but he doesn't seem displeased by these developments-- rather the opposite, I should think by his reactions! I suspect either Nio or the teacher are his informants, because there's no way that teacher doesn't know far more than he's letting on.
The questions don't just come from him, though. The specific people she faces are each part of the challenge, bringing their own carefully-selected lessons of virtue and vice. Like Haruki, who waxed on about Haru [herself] finding freedom only in death. That's not an accident either; the recipient of the message is Tokaku! Surely you don't think the coincident riddle was just a coincidence?
A professor once gave me an object lesson in the power of tests to shape our understanding, from which I arrive at the following assertion: a well-crafted test is one from which we learn new lessons, even as we demonstrate mastery of the material. Tokaku... she wrote an answer to the caged bird riddle. She wrote "death". But after her encounter, she changed her mind. And within this understanding, this means she passed the test.
I suppose I'm probably over-thinking it, but it's fun.
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