I've found a few references to camera firmware updates but no instructions.  In the downloads area this is a file FC200_firmware_v1.2.5g.zip which includes one file named  "firware_plus.bin".  

Is this a camera firmware file and if so, where would I find instructions for installing this using a Windows PC?

I would check the firmware with the app, 1.25g has been out for sometime.
When connected to the app go to settings / about and it will list the firmware.

As for your other question, you update by using the micro SD card.