This feels... wrong, somehow - we wouldn't say that a 100,000lb shuttle transporter hitting you at 1mph will do the same damage as your 3,000lb car at 35mph. There's way more dynamics at play here.
It is kind of wrong. What matters is the force impacted upon the person (their acceleration), not momentum. Basically, change in velocity over time is what really matters, but because momentum is conserved, it influences what the total change in velocity is.
You are right I think, it's about impulse, force over time, surface area and how much energy can be transfered through the surface area through the underlying tissue and create a ripple basically. I suspect that at some point, the 'transfer function' of energy just maxes out and mass of the vehicle itself is pointless over that point, as it's all lethal.
I agree. If I jump up and down and impact the earth with my feet it's quite harmless. I suspect above some lower bound it doesn't matter how much something weighs, it's all about how fast something hits you (because it's mostly you that's being accelerated).
Although the weight (and correspondingly, the size) of a car does play into sight lines, maneuverability and how fast the car can decelerate.