2. can it be programmed to trigger an external flash without flashing its own?
You can always cover it up :-)
3. how long will it live/shoot on its own battery? (sorry, this one is definitely not a CHDK question, but perhaps you just know this)
It depends VERY much on the shooting conditions.
Of cource, the flash drains a lot of power.
The display is another major factor. It can be turned off but (at least in several other cameras) turning the display off disables manual focus. A possible partial workaround is to insert a jack in the A/V out plug. The camera thinks to be connected to a monitor and will turn the display off. The actual display electronics stay on, anyway, so it's only a partial workaround.
Long exposures tend to drain more power, of cource, as some electronics stay on for longer, but that's not that important.
And more obvious factors: shooting more photos will shorten battery life.
Without having a G9 and doing actual on-the-field tests, it's difficoult to say.
Other factors are VERY important, such as temperature. i have taken part in a couple of high altitude ballon launches, and in the first one (in january) I am fairly certain the extreme cold shortened the battery life. In another occasion (a launch in june) the battery lasted for wee over 3 hours, until re-entry. It was a different camera, though, so your mileage will vary.
Anyway, I don't think an external supply would be a problem. In balloon applications, where the TOTAL payload is about 1Kg, heavy batteries are a problem, but in your case I guess it's less a dramatic issue.
Anyway, an external flash will need its power supply too. Depending on the external circuitry (and on the batteries that are on-board in your vessel), you could use Canon's 12V adaptor or any other adaptor that gives the right voltage.
Anyway, if you are thinking ot making a time-lapse of a protist's motion, you might as well consider NOT using a flash, and use long exposures (of several seconds). I don't know the absolute ambient luminosity down there, so I don't know if it's really feasible, some calculations would be needed...
Unless you want a time-lapse that spans through several days, in which case I guess that shooting in deep sea AND during the night really requires a flash.
Have you thought about a LED lighting system? LEDs are usually moe efficient, so it might be easier to achieve long battery life. Of cource, the light is less strong, but again with long enough exposure you could get there.
Really fascinating project....