Small detail about the super diode circuit that bugs me
An op amp can source or sink current (it can go in or come out).

A good op amp is supposed to have high differential gain (it is supposed to amplify the difference in voltage between the two input terminals).

About your schematic

If you have a positive input voltage on the inverting terminal, the op amp's output will go low quickly. At a certain point, the output voltage of the op amp will be lower than the voltage at the inverting terminal by some amount necessary to make the diode conduct (say, 0.7 V). The diode D2 is now forward-biased because there is a positive input voltage and the output is at a sufficiently lower voltage.

The op amp's output will go to a voltage where the diode conducts the right amount of current (which is also flowing through the input resistor R3) so the appropriate voltage drop occurs across R3 to make the voltage at the inverting terminal 0 V.