He has no libido, because it was suppressed, however, that doesn't mean he can't get it up, he just doesn't care enough if he does. His testosterone is very high though. Why no rage? Iron discipline. John has decades of training, and he was far more emotional during his youth. Now he is in control.
All Spartan IIs are like this.
As far as the Cortana discussion. Because their relationship isn't based upon lust, nor is libido a factor between them, he doesn't hope Cortana gets a human body so he bang her.
He might love her in that Big Boss/Boss way.
Maybe 343 will have them f$%&. Who knows? --- They are similar, yes. But like your girlfriend and your sister, someone is gonna be pissed if you mix them up.