Making a new gun for each shot in full on inconsistent.
As long as the trigger was pulled swiftly and with relatively the same amount of force, there should be no problem, and if for some reason it did matter, all he needs to do is go with a short swift trigger pull with more force, and a longer less forced trigger pull and retest..
Heat and humidity? This only matters if you tested in different locations.
Theoretical muzzle velocity? Why? So there can be more error within findings of the spring constant and the friction coefficients?
This sounds like it would be the problem, of course there is going to be lost pressure, the gas wants to fill the area with the least resistance first, that being the looser fit of the darts in the clip.
No, you're not right. Because there is no relationship between what the range should be and the height of the gun.
Please tell me you're joking?
You also speak of square roots and why they have no place? I am not supporting anything said before as it doesn't make any sense at all, there is no constant ratio between initial height and final displacement.