1) Continuous common mode feedback (CMFB) is used together with continuously operating OTAs, whereas switched capacitor (SC) CMFB is used for SC OTAs.
Hope I've understood your question correctly. The answer has nothing to do with the coupling from OTA output to the CMFB input. This coupling can be resistive and/or capacitive.
2) SC operation allows for sample and hold mode, and for low voltage offset operation. Continuous operation cannot offer such methods.