Well, there is a C flat, it’s just also called B. And vice versa for B sharp, that’s just C. There is a half step between B and C, it’s B to C. All the sharp or flat symbols do is signify you should play the half step up or down, respectively, from the decorated note.
The same is true between E and F. There’s a bunch of complicated reasons that the black keys have gaps between them, ranging from the physics of sound, to Western music theory principles, to ergonomics. I’m by no means an expert on any of this, I just think it’s interesting, and a fun topic to look stuff up about.
Oh, I guess I was confused by your wording then. You said there’s no C flat or B sharp, but there definitely are both of those things. You also said there’s no half step between them, but B to C is a half step. I guess you meant there’s no note between B and C that represents a half step up from B or a half step down from C, but it wasn’t clear to me.