Claw dude is Mumhkar, and the white mechon that had been shown once or twice at that point had Fiora as a "pilot."
But all of that is really pretty minor and the general concept of faced mechon would become obsolete by the time you finished the area you were in. You hadn't even gotten into the meat of the story.
At prison island you meet Zanza (who is ultimately the final boss, and is effectively the "soul" of the Bionis), a couple areas later Egil (who is kind of a "trap" boss that the game tries to trick you into thinking is the real enemy, and Meyneth, who is the other god along with Zanza (Mechonis soul) and is using Fiora is a vessel.
Zanza basically lays things out for you pretty straightforward, but you don't know enough at that point to really understand what all he's telling you. He unlocks the Monado so you can fuck up faced mechon, and lets you have at it... because Shulk is actually just a vessel for Zanza. Which makes a lot more sense if you remember back to things like Shulk mentioning two voices in his head, and various things that happen later in the game. And most importantly: his ability to control the Monado. Fiora and Mumhkar attack at Prison Island, but with your super-Monado they're not really a threat at all, and the Meyneth/Fiora combination isn't really after a fight anyway.
So you head to Mechonis from there, kill Mumhkar, and try to save Fiora. You meet Egil, the big baddie of Mechonis, and chase him to Sword Valley. Destroy their base with help from Fiora, and she regains her senses and Meyneth kind of chills in her brain of whatever. From there you further attack Mechonis and reach the head, fight Egil, win, but Shulk refuses to listen to Zanza's voice demanding he kill Egil.
So Dickson, who is actually working for Zanza, shoots Shulk. This puts him out of commision and Zanza leaves Shulk's body. He fights Fiora, then Meyneth leaves her body and the two fight, Zanza kills her and takes her Monado, so he has both the Bionis and Mechonis Monados which is supposed to make him the supreme ruler, and his visions (which are kind of like what Shulk saw) should have been effectively unlimited. The party escapes and Zanza, controlling the Bionis itself, briefly fights Egil and the Mechonis before Zanza destroys it.
It gets even weirder from there. Loritha and Alvis also happen to be disciples of Zanza along with Dickson. Shulk gets fixed up and gets a Monado of his own, Zanza taking his living body as a vessel somehow made him a third wheel in the Zanza/Meyneth duality. Shulk and co take advantage of a wound to the Bionis and head to the interior and beat Lorithia, and Dickson opens a portal to Prison Island. You follow him, kill him, then fight and kill Zanza.
And if you think things couldn't get any weirder or further out there, they do. Alvis is actually a computer, and Zanza (Klaus) and Meyneth were actually two scientists running an experiment. Klaus used this machine which destroyed the universe and created a new one, with that machine - Alvis - as it's effective god. But Alvis gave Zanza and Meyneth (Bionis and Mechonis) the power to basically shape things as they wished, and they created people and machina in their images. Because both of them were now dead,
Mechonis was destroyed and Bionis was decaying, Shulk had to act as an input to create a new universe, and he chose to create a universe with no gods. A universe implied to be ours. And everybody lives happily ever after.