When you shoot these things, what dice do you use? Specifically, what is the agility stat that you add to your appropriate ranged weapon skill for shooting an articulated arm? Or is some other skill / stat combo used instead?

my gut responce is eather exotic (cyber hand) or throw plus agility

OK. But what is the agility? Basic cyberams are agility 3 unless you upgrade / customize them. What about an articulated arm?

Since you are firing remotely, that would be a Command Device action and your Command program would be used in place of the Agility attribute.

Exactly. For more information, just look up the rules for a Smart Firing Platform in the firearm accessories section of the gear chapter, just like the rules for Articulated Arms tell you to do. Unless you upgrade it, it has a Pilot 3, Sensor 3, and Targeting 3 autosoft and is treated as a drone.