Does that mean that Nine knows that Kazuma and Teurmi are both separate in the body, but thinks that both of them are affected by Mind Eater?
Simple answer: no. She thought that Kazuma was just an act, nothing more.
Long answer… well, Amatsumugi was brilliant enough to translate the conversation: (N denotes Nine, K denotes Kazuma, and T denotes Trinity).
N: I didn’t think it would be you that appeared in front of me.
K: It’s been a long time, Nine of the ten sages. Last time when we met… I can’t remember right now how long ago it was.
N: I have lots of things to ask of you, Yuuki Terumi.
K: Is that so? Ain’t that good. I wanted to speak with you about lots of things also. But let me correct you first. I’m not Yuuki Terumi, I’m Kazuma Kval.
N: No need with that bullshit. In the end Kazuma and Terumi are the same existence.
K: No, this is a little complicated. Well, I understand that you won’t admit it since it’s your fatal mistake.
N: What do you mean?
K: Let us begin first by saying what we want from each other. I’ll let you ask me anything. If I can answer it I will.
N: Fine. My first question. Where did you carry the heart to?
K: Ah, you noticed that. I didn’t think that would be your first question.
N: Answer my question.
K: Terumi took the heart. It looks like he always wanted it.
N: For what reason?
K: I dunno. It seemed that he created something, but I didn’t really understand it. It’s because I’m not that good with alchemy.
N: My next question. If you are Kazuma Kval, then where is Yuuki Terumi?
K: In this body. He is inside it and being quiet right now.
N: My third question. Was it you that took away the Mind Eater from him?
N: Then who was it!
K: Someone that you know well.
N: Stop screwing around. What are you planning to do with the Master Unit?
K: … what are you talking about?
N: It was you who said that you would answer. Answer me. Why are you interfering with the Master Unit? Was it for that sake you made Relius Clover and Shuuichirou Ayatsuki summon the Black Beast?
K: Well, well, as one would expect from the Great Mage Nine. To think you would reach to that. I didn’t expect it. I’m sorry, I underestimated you.
T: Master Unit? Summon the Black Beast… what are you…?
K: Have you already come out? And here I thought of surprising Nine by calling you out a little later.
T: Ka- Kazuma-san…! You did say that you would explain everything to her, didn’t you? What is the Master Unit? And making them summoning the black beast… Why are you doing such a halfhearted explanation? Today, weren’t we going to explain to Nine what we are doing to ask her to help us?
N: Could it be… The one that removed the mind eater was…
K: Yes. Trinity Glassfille. It took some time but it’s gone. But there are some effects still there. Terumi can’t merge that well with me. Well it’s no major inconvenience so it doesn’t matter though.
N: Trinity… Why…?
T: I’m sorry, Nine. But listen to me. If it’s continues like this, Terumi will learn to use Mind Eater and then he might cast it on Kazuma and make him kill you. You’re misunderstanding. Kazuma isn’t the same as Terumi. Kazuma has his own conscious and his own desires. We needed Terumi to beat the Black Beast, but now the war is over. Isn’t it okay to return the body to Kazuma now.
N: You were told by this man, weren’t you.
N: You really… really… are a kind girl. Kazuma Kval… No, Yuuki Terumi. I will not forgive you! So, you have finally shown your true nature.
K: So you now know your mistake, Nine-san. While it isn’t wrong that we are the same, we can split our conscious. When you cast Mind Eater, we split, and only Terumi was affected, and I was not marked.
N: Then… This time I’ll cast it on both of you and make you my slaves for eternity!
T: Stop… please stop Kazuma-san. What are you doing? I…
K: Isn’t it time for you to get it? That’s right. Everything was a lie. Too bad for you.
K: You really don’t learn, do you? Even though I’ve betrayed you once already. Let me teach you two something good. The origin isn’t always in the “past”.
N: What… origin… these things…
K: Hey hey hey, that is the Nox that you’ve created, you know? Are you planing on puling it apart?
N: … I’ve created them. Do you think I can’t…?
K: This is why Nine is scary. It’s time for the show! 666th restriction engine released… Dimensional Interference Field Deployed. BlazBlue Activate! Ouroboros! pull her in!
Shikomi is the first rank the girl gets when she joins the okiya. Shikomi do not dress up, they wear simple kimono and tie up their hair. Their job is doing chores in the okiya,helping her elder sisters and going to lessons.