I don't think it's that far-fetched to think that Furuta naturally ended up with Kaneki rather than by way of scheming and string-pulling. He was originally Kijima's partner, who was also an Associate Special Class. Seeing as how Kaneki's promotion essentially replaces Kijima's empty spot, the most natural place for Furuta to be would be as Kaneki's new partner.
And I do agree the most interesting question is in what way they are acquainted with each other. I'm pretty sure that Furuta is fully aware of Kaneki and his 'awakened' persona, although Kaneki I don't think fully comprehends who Furuta is. That said, he will have his suspicions as the mole inside the CCG has yet to be rooted out.
I also think it's interesting to note that the CCG is also aware of the change in personality. At the very least, Urie is aware of it, as on Page 17 he thinks that Kaneki would be very unlikely to visit Hinami given "the way he is now". I hope he really does have some sort of overarching plan to break her out before she is executed. The mercy he showed Tsukiyama, as cruel a method as it was, does give some hope.