You may be able to get live HDMI out from the RX100 II but you would need an HDMI to AV converter to connect to the video transmitter. There may be lag time so that you could not use this to fly beyond LOS. If you are using the 7th channel on your RC transmitter to tilt the camera then you would need another channel or transmitter and servo/receiver to trip the shutter for stills. That is a lot of weight to carry in addition to the RX100 which is already heavy. I don't think you can use the WiFi in the camera because it may be on the same frequency as the Phantom control. The Wifi range will also be limited.
Don't know if the RX100 II will shoot stills and video simultaneously.
One low tech method to shoot stills is to just hold the shutter button down with a rubber band or strap in continuous mode. Use a large capacity card, highest quality jpeg setting and RAW. As the buffer fills up the shot to shot speed will slow down.
You could mount a second tiny FPV camera and transmitter to fly with and to get a rough idea of what the RX100 is seeing. For video you can just start the camera before you lift off.