Thank you, can't say there's anything I disagree with there. You've given me alot to work with, which is good. I suppose I should probably adress a few things:
Firstly, the units. Now, since what I need to express is an increase in conductivity for all forms of energy, no one unit would do. What I need to do here is either provide a value for each induvidual type of energy - which would require there to be that many units, and I don't think there is - or use some sort of all-encompassing unit for energy conduction. Perhaps efficiency or energy input would do. Alternatively, if all of these quantities are in fact comparable, I could always just provide one unit as an example. Hmm… this will require some working.
Anyway, as for cases 2 and 3. My logic was basically this: Ek = 0.5mv2, so - assuming mass remains constant, which in all of these situations, it does - since the children would retain more kinetic energy, they would go faster. This also why they die from falling short distances. 2 built up a greater speed by first running up (perhaps he was startled by 1's predicamnet, or maybe he thought he could he fly), allowing him to go further before hitting the ground. And it just so happened that the ground was a very sharp fence post. 3 was probably just standing too close to the window, not expecting himself to go flying from the kinetic energy produced as a result of throwing the doll.
The "kid with the piece of wood" just ran very fast into a door, presumebly because he was running too fast to easily stop. A piece of wood splintered off and embedded itself in his skull, killing him from the injury. The bath was a straightforward error, easily enough fixed. The hose is just another Ek problem - she was hit in the chest with the equivalent force of a high speed brick. I'll probably add a reference to kinetic energy in there somewhere, as it seems to be a source of trouble.
The rest of your speculation is quite interesting. I could always try not to overcomplicate things by having the condicted energy, say, be restircted only to outside sources (which I now realise would probably turn them black from EM absorption); but then the possibilities otherwise prove fascinating. I'll see what I can do.