No- it is neither centerfire nor rimfire, since it does not use cartridges.
The two types of cartridges used in rifles and pistols are rimfire and centerfire
Let's use the correct terms- BULLETS are the part of a CARTRIDGE that come out of the barrel. .32 Cartridges are now centerfire, but many years ago were rimfire. .32 rimfire guns have not been made in about the past 100 years, and are considered obsolete. There are also several DIFFERENT .32 centerfire cartridges- .32 Auto, .32 S&W revolver, .32 Long, .32-20 revolver, etc.
The standard 5.56 mm cartridge is centerfire. There IS an adaptor to permit the use of .22 LR rimfire ammo for training.
The difference between rimfire and centerfire rifles would be the type of cartridge they use. Rimfire cartridges are an older design. In a rimfire cartridge, the priming compound (impact-sensitive substance that produces the spark to ignite the gunpowder) is located inside the hollow rim of the cartridge case. The firing pin crushes the rim against the chamber mouth to fire the cartridge. In a centerfire cartridge, the priming compound is located inside a small metal cup called a primer, which is made separate from the casing. The cup is inserted into a hole in the center of the base of the cartridge. The firing pin strikes the primer crushing it against an internal anvil to produce the spark. Rimfire cases are made of soft brass so that the firing pin can crush the rim. However, this makes them unsuitable for higher chamber pressures. Centerfire cartridge brass is much harder, because only the primer cup needs to be soft. With the switch from black powder to smokeless powder, higher chamber pressures became commonplace and rimfire cartridges became largely obsolete. The most common rimfire cartridge in use today is .22LR, popular for target shooting and pest control. Due to low cost and low recoil it is probably the most popular cartridge in the world.
Firearms that use rimfire cartridges, such as the .22 Short or Long rifle, small caliber handguns such as the .25 and .32, rifles that use pistol cartridges, etc. These are cartridges that would not generally be suitable for hunting deer and larger animals, usually grouped as "big game".
That depends entirely on the purpose for which you intend to use the rifle. Modern rimfire rifles are usually chambered for either .22" caliber cartridges (shorts, longs, long-rifles or magnums [WMR]), or for .17" caliber cartridges (.17 Aguila, .17 Mach 2, .17 HMR [V-Max, TNT, or XTP]), or a very few for 5mm. Each has different capabilities, but most rimfires are used for "plinking" (informal target shooting), target competition, or small-game hunting. Most rimfire rifles and most rimfire cartridges are less expensive than most centerfires. There are many dozens of centerfire rifles and rifle cartridges ranging from .17 Remington to .50 BMG and .700 Nitro Express. Again, each has its own purpose(s), from target shooting to hunting big & dangerous game. One would be as ill-advised to hunt prairie-dogs with a .458 Winchester Magnum as to hunt Cape Buffalo with a .223 Remington. The correct cartridge for any given rifle is almost invariably stamped on its barrel. If in doubt, consult a gunsmith. DO NOT GUESS OR ASSUME ANYTHING. As to quality of rifles, there are egregiously poor quality and supremely excellent quality rifles of either rim- or center-fire design. Once you have defined your intended purpose(s), seek competent advice and buy the best quality that you can afford. fenianmarksman
Go to Browning.com and use the serial number look up function. You have not provided the model name, whether it is centerfire or rimfire or the caliber. Without that information, can't help you.
Yes, if somebody says ".22 rifle" they almost certainly mean a rifle chambered for the .22 long rifle (or .22LR) round. The .22LR is a rimfire, as are the .22 short, .22 long, .22 CB, the .22WRF (Winchester Rim-Fire), and even the .22 Magnum (properly called the .22 Winchester Magnum Rimfire or .22 WMR). There are other calibers of rifles that use bullets about the same bore size, but they have different names. They are higher-powered calibers. They are centerfire rounds, not rimfires. Examples would be the .22 Hornet; .222 and .223 Remington, .220 Swift, and .22-250.
In this order; centerfire rifle, shotgun, handguns.
No. A .25 Auto cartridge is too fat, and it is a centerfire. The .22 LR is a rimfire. Won't fit, won't fire.
In general, no. The .22 LR is a straight sided rimfire cartridge 1 inch long. The .223 is a bottlenecked centerfire cartridge almost 3 inches long. Totally different. The 22 LR CAN be shot in a .223 by the use of a special adapter.