A few pointers about how much Kudou knows:
1)Mentioned previously: During the 1st 9 Schools arc Kudou shows knowledge that Tatsuya is special, but the way it is said/written implies that Kudou was sadly lacking in CURRENT details. As evidence of this Kazama corrects him about how valuable Tatsuya really is.
2)Throughout the series Kudou and Koichi(Saegusa Family Head) have determined that the 101, which is supposed to be a check on the 10 Family's, has a link with the Yotsuba. They both have determined that link to be Tatsuya and Miyuki but I do not think they have know that Tatsuya and Miyuki are direct descedents of the Yotsuba Main Family.
3)The reason why they don't think that was revealed with Lina's thoughts about Miya.(Tatsuya's and Miyuki's mother) To the world Miya never had children and died after 20 years of being sickly. Remember that Miya was chronically weak from continuously using her power, but answer me this: Besides Tatsuya's experiment, what was she continously using her power on? My guess, with what we know the Yotsuba was like.. it was simply, physical information control by changing the minds of the people that came into contact with secrets of the Yotsuba. Its already been proven that the electronic information control of the Yotsuba is top class, but it would make no sense for people to completely mess up and lose track as much as they have with the Yotsuba Family. You just do not lose track of a family that destroyed an entire nation.(Great Han which is also call Dai Han in some of the translations.)
This is what I think Kudou knows: Tatsuya is a member of the Yotsuba(but doesn't know his real status), is a member of the 101 and was in the experiment of an "artificial magician" operated on Miya and he knows that Tatsuya is the only survivor. Tatsuya's Magics(as known by Kudou): "Flash Cast", Gram Demolition, Far Strike. Kudou knows that Tatsuya has more magic, but since Kudou knows that Tatsuya is an "artificial magician" he considers them irrelevant.
Of course Kudo and Koichi knows that Tatsuya is a genius CAD technician, but don't know that he is Taurus Silver.
This is what I think Koichi knows: Tatsuya is a member of the Yotsuba(but doesn't know his real status), is a member of the 101. Tatsuya's Magic: Gram Demolition, Far Strike. The rest of Tatsuya's magic is unknown, but is assumed to be at 101 level and hence his threat level is manageable.
Neither one of them realize that Tatsuya full power is sealed by Miyuki, that he is a National Strategic Class Magician and has: Mist Dispersal, Regrowth, Material Burst and Elemental Sight. Kudou may suspect something like a personal healing ability due to Tatsuya injuries during the 9 schools, but if so he hasn't realized what it means.