Questions about Dry EEG electrode interfacing circuit
For question 1: 
\$V_S^i\$ will appear at the negative terminal of OA2. At high frequency, the impedance of \$C_b\$ is low, so the voltage on both sides of the diodes approach the same value, thus this is no current, an effectively high input impedance.  For low frequencies, input that differs by more than a diode drop from \$V_{bias}\$ will cause current through at least one of the diodes.

For question 2: 
For true common mode signals, \$ V_s^i  = V_{cm}\$.  Thus, \$V_{cm}\$ also appears at the negative input of OA1.  With the same voltage at both ends of the series combo of Rf and Cf, there is no current.

For question 3:
I think this may be the same answer as for question 1, with the point just made a slightly different way.

Question 4:
As long as there are no saturations -- yes, and that is central to the analysis of the circuit.