The CMFB works this way. Rcm1's sense output common-mode voltage which it is attached to the source of M51 and M52. The gates of M51 and M52 are at the same and constant voltage, generated by the diode-connected transistor M53. If the CM output voltage goes up, then VSG51,52 goes up, and transistors M51 and M52 inject more common-mode current at the folding node (sources of M45 and M46), which decreases the CM output voltage. That's the way that the CM negative feedback works.
Regarding your last question, yes! you can use whatever CMFB topology you want, as long if it is able to meet the require specs of your design. When doing CMFB designing, your principal concerns are: 1) CMFB input range which limits the output swing of the amplifier and 2) stability of the CMFB.