No- the 7x57 was developed separately, in 1892 by Paul Mauser. The 8mm Mauser (actually the 7.92 Mauser, but every calls it the 8mm) was developed by a government board.
Depends on your definition of better. All 3 are capable of taking any game found in North America. The 8mm Mauser carries a little more energy than the .308. The .308 may have an edge in accuracy. The .270 is basically the 30-06 necked down to .27 caliber, shoots flatter, due to higher velocity. This is one of those Ford/ Chevy/ Dodge discussions.
Yes
The .270 is a necked down 30-06. .270 WSM is a necked down .300 WSM. The 270 WSM is faster than the .270, and has a shorter case.
The parent case of the .270 is the .30-06, necked down. The parent case of the .243 is the .308 Winchester, necked down. Aside from the larger diameter of the .270, the .270 has a longer case.
Send me photos of the rifle and of the markings, and I should be able to narrow it down for you. The email address is in my bio page.
The .243. It's basically a necked down .308 Winchester.
The "parent" cartridge was the .250 Savage, necked down to .22 caliber.
no- very much a center fire cartridge. It is the .308 cartridge necked down to a smaller (.243) bullet.
The .357 Sig is a 9mm projectile, loaded into a necked down .40 S&W casing.
There are several rifles, both military and commercial, which have been made for this cartridge. Try to narrow down your criteria to something reasonable.
I believe the smallest bullet in terms of diameter is the .17 HMR. It is a .22 casing that is necked down to accept a .17 caliber bullet.
The .17 Hornady Magnum Rimfire (HMR) IS the name of the cartridge. It is a bottle necked rimfire cartridge- similiar to a a .22 Magnum necked down to .17 caliber bullet. Bullets used in this cartridge may be several different types, but are typically 20 grains or 17 grains in weight.