You will have to define what you mean by fastest. Do you mean the fastest velocity of a bullet in flight, or how quickly it can fire a second or thrid shot? For the fastest velocity, probably a handgun such as the T/C Contender, firing a rifle type cartridge. For rapid fire, there are several machine pistols (fully automatic) that fire several hundred shots each minute. Of course, thre is the mini-gun used by Jesse Ventura in the movie Predator- it fires several THOUSAND shots per minute. But you won't find those at your local gun shop.
A hand gun.
You must specify whether you mean in a long gun or a hand gun.
colt
The .950 JDJ is the biggest rifle The biggest hand held gun is the 600 Nitro Express Pistol
mg 42
You will have to define if you are talking about hand held or crew served.
M2 can be hand held, but, that is the exception. MP5 in 10mm is along the lines of what you might be asking about.
Question can't be answered as written. One hand or two hands?
They could be designed to, but they don't.
A spring gun? It depends on how fast you can cock the gun. There is not a fastest gun.
As of today the fastest gun would be thy gatling gun but it needs to charge up.
The duration of The Fastest Gun Alive is 1.48 hours.