Why are we even arguing these story details? 

Not like they're gonna really matter in the big picture. The only thing I'm seeing is something of a plothole involving faction dominance and tech but this is pretty anime flavored so it's par for the course.

Anyway for the questions pertaining to my gear:
It's a sword and it cuts stuff end of story much like your lightsaber.

Point defense is just like little turret things that shoot at missiles and stuff and are automated. And of course the generic rifle is an oversized gun that shoots large bullets.

The ATA is just the name we gave to this predecessor bot that served as the framework. It's only purpose is as a plot device that briefly explains the origin of the gimmick for the mechs