1) In the unofficially English translated Japanese version, yes, however in the official English version, it's called the "Hyrulean Civil War"
2) Now that you said it, it does say "there was a great war" or something like that in OoT, I think that's where you must have gotten the "great war"...
o_O Huh? Since when was the imprisoning war confirmed as the war before SS? In the old ALttP manual, the sealing war was originally referred to as the "imprisoning war". How is the sealing war/imprisoning war before SS? And where the heck did this "great war" thing come from? I'm confused...
I believe that somehow, the Fallen Timeline is some first existing reality after OoT, then because of ALttP Link's wish, part of that wish somehow linked to past altering it, granting Link true wish and desire, to create a world where the Hero of Time won and the imprisoning war didn't happen...