What is the huge backpack thing on the back of a Pred?

The part at the far back on the left side, that appears spikey, is the med kit. You could be correct about the power supply. It has to be located somewhere in the armor. It could also be in the wrist gauntlet.

I think its the thing that lets the plasma caster roll up and down.

As the title says is probably just his backpack with all the features mentioned above and the rest of his item stock I suppose.