If the thread pattern on the rifle is the same as the brake, yes it will work fantastic. Make sure to check the thread pattern of your rifle before purchasing any muzzle device.
Great question, the Gen 2 is actually the first ever self timing brake and is still a cult classic to this day, the Gen 3 was an updated version with some notable upgrades like adjustable top ports and an extra recoil port. The reason the Gen 3 may be found at a lower cost is because it is a discontinued product as it has been replaced by the new Gen 4 which is more efficient, softer sounding and has extremely efficient top ports making it very easy to dial in a flat recoil impulse. The Gen 1 is gunsmith model that requires timing and blending, the Gen 2 is still a great option and is self timing and a beast on recoil reduction, the Gen 3 was a first revision of the 2 and the Gen 4 is king.
Yes the 45cal variant is for a 45-70.