Like anything else it depends on the brand, the model and the condition of the rifle.
Is it still working. Is it in Poor, Fair, Good, Very good or Excellent condition
Not normally unless you are using the wrong size pellet. Example: you have a .20 caliber rifle and you put in a .177 caliber pellet. Then Yes it will fall out. Check the barrel of the rifle and see what size pellet it uses
It all depends on the current condition of the rifle. And is it still working. With out more information about the condition it is not possible to answer you. And I think you mean Rifle not Gun.
20-100
Around $100 in good condition.
The Sheridan Blue Streak air rifle uses a 5mm pellet. This is about .20 caliber- larger than the .177 pellet, smaller than the .22 pellet. I have been able to get these at Bass Pro Shop. There are also at least 3 lots of them for sale on Ebay right now. Only the 5mm/ .20 caliber pellets will work in your rifle- do not try to substitute anything else. P.S. Have had one for years. These are extremely good air rifles- very accurate, very powerful.
BB Guns are not designed for hunt. For hunting you will need a pellet rifle. preferably a .22 caliber pellet rifle. BB guns are designed for just plinking around and are not very accurate beyond 20 feet.
20-100 usd
Which model. Benjamin made about 20 different models. Also state the condition of the rifle.
No it's larger, and a .22 is larger than a .20 Pellets come in these sizes. .177, .20, .22, .25, 9mm, 45 caliber and 50 caliber. The last 3 sizes are for big boar air rifles.
20-2000 USD depending on specifics
It's not so much the caliber you want, its your selection of pellet design. A .177 is sufficient to hunt birds but I would select a hunting pellet (hollow point) to use in the rifle. Hollow points will deform on impact and make a clean kill. .20 and .22 pellets have a little more knock down power but the .177 will have a slightly further range. On the other side .20 and .22 caliber pellets are slightly slower in (FPS) Feet Per second, they, because of the addition weight of the pellet, will fly straighter in a crosswind then a .177 pellet.
It all depends on the bore size, and if you really mean GUN as in "gun or rifle." The larges Pellet bore is 50 caliber and that would be a Air Venturi .50 Cal, 275 Grains, Solid Core, Soft Lead, Round Nose pellet. If it's just a pistol it would be a .22 caliber pellet and that would most likely be a Predator Big Boy Senior .22 cal, 28.5 Grains, Domed. Remember air gun/rifle pellets come in all sizes. .177, .20, .22, .25, .9mm, 357mm, .45cal and 50 Cal.