QKD - Does BB84 Protocol rely on a prearranged code?
Bob and Alice then take the correct configurations, and they convert those to a prearranged code, which could be, as an example, that a correctly guessed diagonal detector is 0, and a correctly guessed rectilinear detector is 1. This way an encryption key will be composed.
  


I believe that's where you got it a bit off.  A correctly guessed rectilinear detection is not a consistent 1; instead, they might have the convention that a horizontal polarization is 0 and a vertical polarization is 1; similarly, a 45 degree polarization might be 0 and a 135 degree polarization might be 1.


  If Eve listens on the public channel, and gets both Bob's measurements...


Eve most certainly does not get Bob's measurements.  Bob does tell the world (well, Alice, but we can assume Eve is listening in) what he set his detector to (whether it was on the horizontal/vertical setting, or whether it was diagonal), but Bob certain doesn't tell what the detector actually measured.

So, suppose Alice sends a rectilinearly polarized photon to Bob.  If Bob set his detector to rectilinear, he'll tell that to Alice (after the photon has been detected); Alice will tell Bob that his guess was correct.  Alice knows what polarization she sent, and Bob knows he measured it correctly; they both know whether it was a horizontal photon (a 0), or a vertical photon (a 1).  Which is it?  Well, neither Alice or Bob are telling.  Someone in the middle can't be sure (unless they tried to measure it themselves; in that case, there's a chance that they got the polarization wrong when they re-emitted the photon, and hence will introduce detectable errors).

My opinion: I don't personally think this QKD stuff is actually practical (that is, it doesn't solve any problem that can't be better solved using more traditional methods), however it can work.