Op amp problem - unexpected simulation results
A: The linked article explains that the op-amp / diode combination eliminates the normal voltage drop associated with rectification. For a small signal a regular diode's \$ V_f \$ is too high and would either distort or block the signal. Putting it into an amplifier with feedback eliminates the effect of diode voltage drop.


  What is the point of this so-called super-diode, where the last stage has already been off-set to vcc/2? (meaning the signal from last stage are all positive).


The purpose of section A is not signal rectification but rather peak envelope detection in conjunction with C3. The signal is at positive voltage all the way through. The peak detector will be biased above \$ V_{cc}/2 \$.

B: This is a standard non-inverting amplifier operating around \$ V_{cc}/2 \$. This is standard practice in audio circuits powered from a single-ended supply.