Will my 5.5" CS function via the HDMI port as a standalone monitor for my Mirrorless Sony camera.

Initially connected and switch the HDMI setting and so far no image from the Camera.

Any suggestions would be appreciated.

The HDMI connector on the CrystalSky is an output...it is not an input.  There has been talk of making it an input through a firmware update.  I would not hold my breath.  I am not sure the hardware could support this in any case.
It could be possible to build a dongle that converts HDMI input to USB and connect that into the CrystalSky.  The USB is both and input and output.

Ray