1) Where is your schematic of a Mosfet amplifier that shows C1, C2 and Cs?
2) Where is your schematic of the opamp showing the resistor?
3) Where is your schematic of ..... ???
It is easy to upload schematcs so that we will know what you are talking about.
Shermaine loves to make people guess at his questions. See if you can guess at these answers.
1) C1, C2 & CS are determined by bandwidth & stability considerations.
2) Usually to first order compensate for the offset error introduced by the input bias current flowing into the "-" terminal. Yes, it improves offset due to Ib but adds noise to the circuit (Johnson/Resistor noise)
3) High common mode rejection, High current source output impedance and/or for biasing other stages.
C1 forms a highpass filter with the source resistance in series with R1 and R2 in parallel.
C2 forms another highpass filter with the 10k load resistor.
Cs forms another highpass filter with Rs.
Each highpass filter reduces the response at the cutoff frequency by 3dB. Lower frequencies have their response reduced more.
For the opamps, R1 compensates for the bias current in R2 and R3 at the top, and compensates for the bias current in R4 and R5 at the bottom.
R1 is not needed (connect directly to the input with wire) if the opamps have FET inputs.
The inverting input of the bottom inverting opamp is a virtual ground. Look in Google.