This doesn't seem legal and especially for hunting. I can imagine someone has created one but is probably not cheap due to the fact it would be custom made. Sorry if I didn't answer your question
No. the longer barrel will preform better.
Yes
Long barreled shotgun
Gun shop, gun show, Shotgun News, Gun List
Yes.
No, according to RCW 9.41.190: "It is unlawful for any person to manufacture, own, buy, sell, loan, furnish, transport, or have in possession or under control, any machine gun, short-barreled shotgun, or short-barreled rifle; or any part designed and intended solely and exclusively for use in a machine gun, short-barreled shotgun, or short-barreled rifle, or in converting a weapon into a machine gun, short-barreled shotgun, or short-barreled rifle; or to assemble or repair any machine gun, short-barreled shotgun, or short-barreled rifle." You can thank the assault weapons ban for this. There are exceptions though: http://apps.leg.wa.gov/RCW/default.aspx?cite=9.41.190
A hand gun.
Double barreled shotguns are manufactured in several countries.
A musket is an old fashioned, smooth barreled long gun.
The Minigun is Gatling gun where the barrels are powered by an electric motor. The Gatling gun, was a hand cranked, multi-barreled gun.
30-40 years.
3 or 4 are possible in the case of a multi barreled gun, but more than 2 is quite rare.