NO
1956
The 44 Magnum made by S&W acutally uses a .429 diameter bullet. I am unaware of any .44 diameter bullet loaded in a round called "44 Magnum"
I'm not aware of a .45 Magnum. There is a .44 Magnum. The 44 magnum is typically a revolver round, very high power. The 45 ACP is typically used in semi-automatic pistols. The 45 ACP is not as powerful compared to the 44 magnum (mostly due to the amount of propellant in the 44 magnum compared to the 45 acp).
.44 Magnum
.50 - 5 USD depending on the load
No, you cannot. The .38 Special can be fired out of .357 Magnum revolver (but not automatics or lever action rifles), however.
In a .44 Magnum revolver, yes. In a semi-automatic .44 Magnum (such as the Desert Eagle), no.
It can use either 44 magnum or 44 special
Yes. The 44 magnum can fire 44 special ammo in the same way a .357 magnum can use .38 Special.
No one currently, though the M1 Carbine has the equivilant power of a .357 Magnum, and that's a semi-automatic. The .44 magnum is in an entirely different class than the .357 magnum or the .30 M1 Carbine rounds (not at all the same as the MI rife 30-06 round). I'd look for a used Ruger...preferring the "Deerstalker" style to the model 99/44 "Deerfield" carbines...because though the Deerfieds are newer, they simply are not made as well as the old Bill Ruger .44 carbines. I have had to trail far too many deer crippled by the .357 magnum, to have much respect for it as a hunting round. Deer hit with a stout .44 mangum round, do not usually go very far. I have gotten dozens of deer with the .44 magnum (pistol and Rifle), and it simply is a great performer on deer.
The term magnum was first used with the .357 Smith & Wesson Magnum (to use the entire name) to designate a cartridge that had higher energy than the parent catridge it was develoepd from. In the case of the .357, the parent was .38 Special. In the case of the .44 magnum, parent was .44 Special. A magnum is a bottle of champagne that is larger than a standard bottle, and the word was borrowed by the firearms world.