1. If there is a member of dispatch staff on the platform would you expect them to be sufficiently trained in the particularities (eg pits and plungers) to take control of the situation, and obey their instructions?
As discussed above, emergency train stop plungers on the platform are limited to a very few tube lines - possibly currently only the Central line - so won't be generally applicable.
2. If I need to wave my hands in the air, am I aiming to catch the attention of a. the driver through the cab window, b. the driver through the CCTV in cab, or c. a CCTV operator elsewhere?
3. At which point on the platform is it best to stand when waving?
IIRC the standard emergency stop signal is simply to hold both arms straight up above your head. It doesn't involve waving, specifically. (There is an alternative, night time signal of vigorously waving a light, which was discussed above, though.)
Remember, though, that a driver would normally expect any handsignal to be given by someone wearing hi-viz clothing. I'm not sure there's any "usually" about it's use, so I doubt there's any standard place to stand. It will all be down to your judgment of how much sighting time the driver would have to see you and respond.
If it were me, I'd strongly encourage other passengers to move clear of me, so I stood out from the crowd, and face the train and try to catch the drivers eye. Given that I wouldn't be wearing hi-viz, the object is to make what would be a someone unconventional signal as clear as possible.
EDIT: If you're talking about signalling "do not dispatch" or signalling to a train that has just been dispatched (and just started to move) then I don't think there's any standard way to do that in most circumstances (although during LUL platform dispatch, I believe the dispatcher can do that by lowering the bat). The handsignals we're talking about here are _intended_ to be given by railway workers to approaching trains, and are essentially the equivalent of a red signal. Although if there were clearly and deliberately given to a train on the platform from behind, the driver may well understand the intention (as drivers in this thread have indicated).
4. In terms of stopping distances, what proportion of the platform does the tube train need where the driver initiates an emergency stop on entering the station?
I'm not sure there's any one answer to this - it will depend on the speed of the train, to some extent the class of train, and of course to adhesion conditions. In the case of a train not scheduled to stop at that station, there's very little chance of it being able to stop within the station in response to a signal given from someone on the platform.
5. Where on the platform are the plungers?
On the Central line, there are clearly labeled "emergency train stop" plungers at intervals on the platform. They are intended for public use and there therefore clearly labelled and quite conspicuous. They don't exist on NR, or on most other tube lines.