Probed pads are a trim, using a series of fusible links ( you can see a few have been detonated). clockwise from top you can see 1, 4, 10 have all been blown open to add the diffused resistors into the circuit. The other pads are associated with the bonding pads so they would not have probe damage on them when bonding.
2 bond wires so it can do output sensing without the resistance of the bond wires having an effect, and the other is to reduce bonding resistance. the pads in both cases have a low value aluminium trace connecting them, but the bond wire resistance will be lower than this so it does help. The NC pads seem to be there to add resistors later after encapsulation, probably used to do a final trim for either tempco or output voltage, as the top layers are all associated with the trim pin in some way, adding in resistors so you can do a trim up or down depending on the fuses blown.
Nice photo there, thanks.