Without going too far off-topic...
I suppose it's on-topic as long as it's relevant to determining the amount of recoil one can expect from barrels of different lengths.
Rate of acceleration and the force required to achieve it. Recoil is nothing more than backward acceleration in response to the bullet's forward acceleration.
Technically, isn't recoil defined instead as impulse, which is basically the momentum imparted by the bullet to the firearm and the shooter? It's more like a total of something as opposed to an instantaneous measure of acceleration or force, at least the way I was using the term. In that case, by the law of conservation of momentum, recoil would be the mass of the bullet multiplied by its velocity (applied in the opposite direction), meaning that shorter barrels would indeed result in less total recoil, all else being equal (and a louder blast from wasting more gas and energy).
Yes. The gun is in full recoil before the bullet exits the muzzle.
By "full recoil" you are apparently referring to the peak reaction force applied to the gun, which does indeed have a major effect on how recoil is perceived, but it is not recoil per se, as I understand it. We could say that barrel length has no effect on the "snappiness" of a particular load, if this is the effect of the peak force, but then again perception is complex, and for example higher actual recoil may combine with the same peak force to be perceived by some as being "snappier" even though it is not (.40 S&W versus 9mm may be an instance of such a phenomenon).
With some fast powders fired in long barrels, it's entriely possible for the bullet to be moving faster before it exits the muzzle than at the time of exit...and it was proven some years back with a 26-inch .308 rifle by lopping off an inch at a time and firing different handloads with various powders at each increment.
Absolutely, that's what happens when there is no longer enough gas to pressurize the barrel sufficiently to overcome friction.
Typical handgun powders hit peak pressure/force and acceleration rapidly... within a half-inch of bullet movement. Some really fast powders...like Bullseye...will do it before the bullet base has even cleared the case mouth.
That may true for the peak pressure/force and acceleration, but in typical handguns the bullet will still accelerate through the whole length of the barrel, and the shorter the two barrels being compared are, the more significant the difference in bullet velocity and recoil impulse will be between them.
Quick example, and using round numbers for simplicity.
If we assume 30 fps per inch of barrel gained or lost, and using a 4-inch .357 magnum revolver for the example...158 grain bullet at 1250 fps...we're getting 120 fps from the barrel. That leaves 1130 fps unaccounted for.
I think that's quite way off, even for a simplified example. Refer to the following tables for actual data:
http://www.ballisticsbytheinch.com/357mag.html
http://www.ballisticsbytheinch.com/38special.html
As you can see, even the difference between 4" and 2" barrels (the lengths in your original example) is quite a bit more significant than you're suggesting (based on longer barrels, I realize, but the truth is the truth). Quite simply, the bullet is accelerated for longer and to a significantly higher velocity in a 4" barrel than it is in a 2" barrel, and therefore the resulting impulse is significantly higher (what I said originally) even though the peak reactive force should be the same (what you just said).
Now, how this difference is perceived by the shooter depends on the individual and is a complex subject, especially since even a couple of inches of barrel length can add substantial mass to the front of the gun, which also changes its balance. But I do think that recoil is lighter, at least in one measurable parameter--impulse, which normally defines "recoil"--when a gun's barrel is shorter.