1) I prefer using Pro Tunes as you have more ability to adjust the quality of the video. Think of it like a "raw" photo (Pro Tunes on) vs jpg (video with Pro Tunes off). Personally I have found my videos to be very easy to color correct with the "auto balance" button and occasionally need to use the more in depth color correction features in FCPX.
2) I shoot using the Polar Pro filters or Oculus filter with Pro Tunes on. Keep in mind you only need red filters if deeper than 15 ft or so. As you go deeper you lose colors in the spectrum which you cannot bring back in post production editing. That is why the red filters are useful. You can always remove some color but never add what is not captured originally by the camera.
3) I exclusively use 1080p 60 fps and play them on my 46" Samsung TV all the time. Makes you feel like you are "in" the dive! : )
4 & 5) I have filmed short clips and left my camera on through the entire dive, which is my preference. The reason I prefer leaving the camera on throughout the dive is that you never know when that "money shot" will appear and what if the moment you go to turn the camera on you scare away the fish?? I have also found since scenes happen so quickly you cannot react and line up fast enough. This is also why I where the camera on my head. That way whatever I am looking it will be in the film. The batteries normally last 90-120 mins. I do not use the backpack screen, that sucks up the battery too quickly and since I wear it on my head, no point. If you are holding the camera in your hands than the LCD would be useful and limits you to about 45-60 mins of battery time. The LCD would be helpful if you are using it with your hands to be accurate that you are getting what you want in the frame.
6) Depends on how you plan to use it in the water. I have mine secured with a beany cap over the head strap and therefore it is lined up so that it captures what I am looking at. The LCD would be helpful if you are using it with your hands to be accurate that you are getting what you want in the frame.
Check out some of my Go Pro videos and you can see my setup in some of them and how 1080p @ 60 fps w/ Pro Tunes on and off looks.
Polar Pro Snap on Red Filter for Go Pro Hero 3 - Black Edition & ProTunes On - YouTube
Underwater Huntress
www.UnderwaterHuntress.com