There is no "best caliber" because it depends on several things. If the child is new to shooting, a .22 is probably a good choice. They don't have much recoil, they are easy to shoot, and ammo is cheap. Many people start beginners on .22s.
It all depends on you, your pocketbook, your skills.
Best to ask a gunsmith for help
Can't be answered without knowing what caliber, intended use, make of firearm
Yes, colt makes a few different versions of the 22 caliber handgun such as the Woodsman, and Challenger.
Assuming you mean a bullet fired from a .22 caliber handgun, the answer is, yes, it can, but it depends on several variables.
Its the size of the bullet that the gun is made for. its the caliber that a handgun uses
It should be marked as to caliber on the barrel.
No.
Probably. It would likely refer to a handgun that fires a .45 caliber ACP, or .45 GAP or an older .45 caliber revolver round.
.32 caliber. In a semi auto handgun, probably .32 ACP
45 has the larger projectile. Size of the handgun will vary.
There is no one single best caliber, but to get an answer, you need to be a little more specific. Rifle or handgun? Define long distance. 50 yards? 100 yards? 1000 yards?