Arms Don't move independent

The problem is that you have two Dragger behaviors applied, one for each arm. The way Dragger works by default: when you click it looks for the nearest Draggable handle within its hierarchy and grabs that. Since you have two Dragger behaviors, each one is doing that. And since each behavior "sees" only the Draggable handles in its part of the hierarchy, when you click and drag each one says "oh, the closest handle is the one in my arm, so I'll drag that" — and then they drag at the same time.

So there are two ways to fix this: if you don't actually need two different Dragger behaviors, just remove (turning off isn't enough) Dragger from each each arm and apply it to the root of the puppet. Then you have a single Dragger that can see which arm is closer to wherever you click. (If you have a behavior at different levels of the hierarchy, the inner one blocks which handles the higher-level one can "see".)

OR, if you actually want two Draggers (e.g. you want one to be set to Hold in place, and one set to Return to rest, which indeed you have done) enable the Limit Range checkbox on both Draggers, and adjust the Range if desired. If you click within that distance of each draggable handle, you'll grab it, otherwise you won't.