If it is not marked on the rifle, the only certain way is to have a gunsmith make a casting of the chamber. This uses a material known as Cerro-Safe, which melts at a very low temperature, and shrinks a minimal amount when it cools and hardens. The smith will plug the barrel, melt Cerro-Safe, pour it into the chamber, and after it hardens, push it out. The casting is then measured with a micrometer, and the measurements compared to known cartridges.
Take the rifle to a gun shop so they can figure out what make, model and caliber rifle you have. There is no 84 caliber long rifle.
a .22 caliber
You will have to contact the company to find out.
A .177 caliber air rifle has very little recoil.
.223 caliber or 5.56mm.
No You could build a rifle in .306" or any other caliber but you are likely referring to 30.06. A 30.06 rifle is referred to as "30 Caliber" but to be accurate it is nominally .308"
Yes, I can. A Barrett M107 is a .50 caliber sniper rifle.
Basically impossible to do with just the serial number.
Professional appraisal
Many do, but, not all the time. You will have to call to find out.
The Dragunov (note corrected spelling) sniper rifle is in caliber 7.62x54mmR. This is the same caliber at the Moisin-Nagant 91/30 rifle.
In the States, a 50 caliber rifle can be acquired after filing certain tax stamps. Once the tax stamps are paid and a background check has been cleared, then a 50 caliber rifle can be purchased at some specialty gun stores.