Help with analysing OP AMP circuit
I think I can help partially, but I'm not sure.

1) The reason for providing 2.5VDC offset has to do with the way the OP is feeded. In this case it's not simetrical but goes from [0;5] instead of [-5;+5]. From this circuit I understand that the objective is to have a sine signal but always possitive.
3) The objective of 4.7K and 100K resistor is to reduce the initial sine Wave which I suppose is 5V.

What I suppose from this is the initial process is to reduce the signal and then shift to only possitive voltage.

Hope this helps you. As for the 2nd quiestion it's a differential resistor, but can't see it's use without a simulation.

PD: It's a fun circuit.