No.
the are also chambered for the 38 caliber, 9mm caliber and 22 caliber
no
It depends what mechanism they use. An air pistol which uses compressed air would work, but any mechanism which needs ignition (e.g. a traditional firearm where the bullet is propelled by gunpowder) or an external air source would not.
Neither is "better". They are each fine in their own right.
Caliber refers to the diameter of a bullet (bullet is the part of a cartridge that is fired out of the gun). A .223 caliber bullet is .223 inches across. It is normally used as a rifle cartridge. a .45 caliber bullet is more than twice as wide as a .223, and is usually used in pistols. The .223 is lighter- it weighs about 1/4 of a .45 bullet, and they are different shapes- .223 is usually pointed, the .45 is rounded.
Which .45 handgun are you referring to? The .45 Colt revolver (Peacemaker) goes back to about 1873. The traditional "45 Auto" was adopted by the US Military in 1911, but there were other, earlier .45 caliber automatics. And of course, .45 caliber black powder ball and cap pistols, ball and cap revolvers, etc are MUCH earlier than the Peacemaker. So... which handgun?
45
Jukar indicates a modern reproduction of a muzzleloader- but there were pistols and rifles- and you don't tell us what you have, or condition. These are fairly low cost- rifles are about $150, pistols about $80
The Colt M1911 and the colt M1911A has only 1 caliber .45 or 45/100 of an inch. This round is also known as the colt .45 A.C.P. (all Colt pistols) It is a short round which differs from the .45 long round.
.45 caliber
If your question is can citizens of the US own a .45 cal handgun, the answer is yes. MOST of the US does not require a permit to own a firearm, and even the areas that DO require permits do not ban the .45. In some countries private citizens may not own a handgun in a military caliber, but the US does not follow that practice.
No. The AK-47 fires the 7.62x39mm round, which is of the .30 caliber, smaller than the .45 caliber.