From a benchrest.
You have to work up the most accurate load for your particular rifle. Each rifle will respond differently to changes in bullets, powder charge, seating depth, etc. What is an accurate load in one rifle may shoot poorly in another and vice versa.
in most cases with match grade ammunition a moisen nagent is capeable of up to 1500 yards of accurate distance
Each weapon will exhibit a preference for one or more brands and bullet weights. You have to shoot as many as you can aford to find out which one your rifle will like the best. There are 300 USD rifles that shoot as well as 10000 USD rifles.
Very generally speaking, a .22LR can travel more than a mile, but with accuracy, most people can shoot out to 300 or 400 yards with one when using a rifle, however some people are accurate further than that.
Anschutz and Remington 700 are regarded to be most accurate rifles in the world. NOMAN
Custom built
Depends on the firearm, what you are shooting, and where you are. With a rifle, firing from a supported position, such as a benchrest is the most accurate. In the field, the prone position is most accurate. However, that does not work well if you are in waist deep grass, or duck hunting with a shotgun. With a handgun, a two handed shooting stance is most accurate, and using a support makes that better.
Impossible to answer as asked. Rifle, pistol, shotgun? What does accurate mean to you?
It is often accepted the Heckler and Koch PSG-1 is the most accurate sniper rifle in the world.
It depends on the Country where you live. However most locations have seasons for hunting Doves and will require a license to shoot them.
In most places, no.
Too broad to answer. At what range? Rifle, rimfire, pistol, revolver? In general, a heavy barreled target rifle (most are custom builds) in one of the 6mm target calibers would be the most accurate to about 600 yards, but other rifles such as the .338 Lapua will be more accurate at 1500 yards.