B: Think about it this way; when you cut the keima "at the waist" (I still don't understand why it's the waist, btw), you take a loose connection and turn it into a standard crosscut. If you understand why crosscutting on the second line is usually a bad idea, you should understand why a keima from the third line to the second line usually can't be cut.
In the center:
Against the side:
(The difference, if it's not obvious to you already, is that
at "a" is a move that strengthens W in the first two diagrams, but it captures the cutting stone in the second two.)A: I can't give you a confident answer, but I want to record what I think so that when someone more awesome explains, I learn from my mistakes.
on both sides, which means that he can make a severe attack against white's 
approach. Of course there are many possible continuations, I've shown one that exemplifies the kind of severe attack that black can make.
white stones. If black pincers, white can make a counter-attack by leaning on black's stones on the left, then counter-pincering 
with 
