Expect the unexpected, then when something mundane happens... you'll be surprised.
I meant to use a standardized gravity on a stage. This can either be a calculated value or you can just say "assuming Earth". It's more interesting to calculate it, though, so do that and then compare it over several stages (as you suggested) and see if any stages, in particular, stand out. There will likely be a common gravity that you'll find.
In this same way (well, similar really), you can also calculate the friction of the stages in Omega mode, if you wish. They are different from stage to stage.
Impulse is the change in momentum, yes. I prefer [I = Δp], its more general.
Yes, you've got the right idea.
Consider that thunder discharges around Pikachu in a half-circle area around him, and for the sake of the problem, pretend that the energy is evenly distributed over the area of the circle. You know how long the hit box lingers, so Pikachu is discharging a set amount of energy over a set amount of time that results in a set amount of launch power. If an object starts from rest and gets propelled outward at a certain velocity, then you have a change in Kinetic Energy. But only a portion of the energy would, in theory, be getting transfered from the thunder strike to the target as they would not cover all 180 degrees of the half-circle around Pikachu.
That change in KE came from the electrical discharge causing kinetic movement (usually, the electricity isn't causing you to move but creating other affects in the area around it that push you after the fact, but that's getting overly detailed). Work backwards from there to find the energy of the thunder or its power (since you know how long thunder lasts frame to frame).
You can send it to me in a PM.
