Okay, I'll take a stab at a few of these:
1. What the difference is between cast and forged, and which is better
Typically, forged is better, but this is a matter of the care taken in manufacturing processes. And, there are several different types of casting which plays a factor here as well.
In traditional casting, molten metal is poured into a mold, filling the shape of the mold cavity. When the metal cools and solidifies, the casting is removed from the mold, and usually goes on for some sort of finishing operations (i.e. heat treating, removing excess material, drill and tap...). Molds in this case can be one-shot items (sand or ceramic) or permanent (die-cast, like a bullet die, only for larger parts).
It is possible to create high strength, high quality parts with casting, but it is fairly difficult. When metal is poured into the mold, and foreign particles in the pour or on the mold surface will become imbedded in the casting (inclusions). Then, there is also the problem of porosity. This is when gas is trapped in the casting, either being drawn in during the pour , or if gassing is used to force out other impurities. Another problem could be shrink, where the metal cools, pulling at thicker parts of the casting, which causes voids and cracks. In the case of any of these three problems, inclusions, porostiy, or voids (also refered to as shrink porosity), when the casting is put under stress (in this case, the gun is fired) stresses are magnified at these faults, which causes fault propogation, which causes the part to fail.
Think of a bridge collapse; the bridge is very strong, but if a cable snaps, the nearest cables suddenly have to carry more load. If they fail, the next cables carry even more, and the failure moves right down the line until the bridge collapses. The same thing happens when a metal part breaks. Stress is applied to the object. The stress is magnified at the edges of a void, crack, inclusion, or bubble. The stress is to much for the surrounding material, which results in the defect expanding. This causes even more stress at the edges, which causes the defect to expand, which causes even more stress at the edges, which causes the defect to expand, which causes even more stress at the edges, which causes the defect to expand, which -BAM- the part fails.
Forged parts are typically stronger because they often start with a casting, then physically force the defects up to the surface, where they will usually be removed during finishing (machining). When the part is heating, and repeatedly struck with the hammer, it causes the internal material to shift back and forth, and the atoms settle into better alignment. Impurities are forced out, voids and cracks are mashed closed, etc...
Both cast and forged parts are often heat treated, which alters the grain size (crystal size) of the material, which affects its physical properties as well.
3. Why Garands have gas problems when they are chopped down. (too much cabbage?)
Garands are tuned to operate at a specific barrel length. When the round is discharged, the gas expands at a certain rate, accelerating the bullet down the barrel. Towards the business end of the Garands barrel, there is a port which bleeds off some of this expanding gas to operate the action. This gas must be at a certain pressure, and that pressure must be exerted upon a piston for a specific amount of time, therwise the action will not cycle properly. If the barrel is cut down, it screws up this system. It could probably be fixed with different port design, but its really a question of tuning. Once something works nicely, i.e. everything is tuned up, don't screw with it.
This is like tuned pipes for automobiles. Well matched and tuned exhaust pipes will help get more power out of an engine. Poorly tuned pipes are a detrement.
You know how people's VCRs blink 12:00 because they don't know jack about electonics? Does anyone else feel the same way about guns? 
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