1. IF you shorten the stock, the gun will "shoulder" quicker. Many bird hunters, sporting clay shooters, and tactical shooters shorten the stock for this very reason.
2. THat depends on the make, I believe you can cut the Mossberge stock down without trouble, but you better check with someone who knows for sure.
3. I don't think you would want to chane the angle. This would most likely result in very awkward shouldering and if you got used to it, you'd be ruined for any "normal" shotgun.
I would think that it would aslo "focus" recoil at ne point or another.
4. That depends on what you want to do with the gun. A trap shooter "fits" a gun completely different from a bird shooter. there are a number of arcane measurements and formulas that stock-fitters can use, but the best ones in the business just observe you shooting, make some modifications, observe you shooting some more, make some more adjustments, etc, etc.