hm...his extreme honesty is much more typical of a gryffindor. however, i got the idea that perhaps you were trying to express that perhaps he was at times a bit brutal with his own opinions. Now thats a different matter. But honesty, as a whole, doesn't always work well for a slytherin. give some thought to that. their biggest motivation is preserving the traditional way of life, and if they have to perhaps not be 100% straight up honest with that, it generally isn't a moral dilemma for a slytherin. they have no problem presenting a lie and making it look like their version of the truth. am i making sense?
as for the pureblood/halfblood thing, why not try a twist on it? he does need to be halfblood since he is not a canon, but...you could have the family living as purebloods and saying they're purebloods when they're really halfbloods b/c they're ashamed they're not purebloods.
one of the most important values for his family to have is tradition. they need to believe in "old fashioned, conservative" wizarding values. consider lucius malfoy. he didn' consider himself evil. he merely believed that things should be done the way they always were--with pureblood wizards--because thats the way it always had been done. perhaps kai's family is a family of old money, with old values and he comes from generations of slytherins, etc. etc.