Not sure about kodachi - The larger varient of the katana was a no-dachi.

I admit, I havn't read it all, but it's late at night and reading through all that is just... blah, not possible for me at the moment.

Katana isn't the name of the weapon; the sword is literally called taisho (katana being the Japanese for 'sword', which ended up becoming a well-spread term in the West for the weapon).

Katanas were next to never actually -used- in open war-fare, considering their poor use as a weapon. Even leather put up decent resistance against the draw-cut style used with the katana, and therefore, samurai were far more likely to use the yari, naginata (especially amount female warriors, or the warrior monks, sohei) or dai-kyu.