Very interesting observations
My impression is that Takuma prefers at that point not to explain further his choice (?) to stay with Sara … like it was convenient for him the subject about him and Kaname which brought up by Senri …
Takuma's case is really interesting and during the charpters I have also changed my opinion about Takuma staying next to Sara. I think that he stays for his own purposes but he does not serve his purposes with Kaname, therefore as you say he avoids explaining his attitude.
Kaname on the other hand know about his choice to stay with Sara and I think that Yuuki also knows it since Maria informs her at the latest chapter that Takuma did not appear but seems to be still under the influence of Sara.
About Kaname's silence, he has no reason to get involved in Takuma's case. He can only respect his friend's wish to stay with Sara (either he suspects or anything like that Takuma's any real intentions).
It's Takuma's purposes that we do not know yet but I think that she controls him perhaps in a way where he does not even realize how much she does. He seems to disagree with her (Harem, the President) but on the other hand little resistance he really shows to her plans (if any)...
Now about Yuuki, I think that she knows certainly about Takuma's and Sara's relationship as most of the vampires seem to know it by now. So she invites him in the academy, despite the knowledge that Sara must be some under some kind of plan by recruiting that girls.
Aido did mention that since these girls agreed on that, there is nothing that they can accuse Sara for (apparently and the hunters attempt to collect evidenve against Sara did not work that well).
But they were all aware that something is wrong as Aido-Dono had visited Kaname and had asked him to reprimand Sara for that reason.
So Sara's action seems to be known- only that she can not be accused for it by now.
Now Sara getting in the academy and being under Yuuki's, Cross and Zero's surveillance is a very bold action. Unless she thinks that she can manipulate them all so well that they will turn against each other, as chess pieces that eat each other.
I think that her target can be Yori (Yori's role has been upgraded at the second arc or is it my idea?). If Sara gets Yori and hurts her- she can blackmail Yuuki, she can hurt the academy by exposing the fact that Cross failed to keep vampires under control and so the humans will not support the academy anymore and she can turn hunters againts vampires (since Yuuki will also have failed).
Of course that's only one way of the many that the script can go but it's likely..