12V Gnd needs to connect to Arduino Gnd.
Wouldn't this potentially burn out the device depending on the amount of electricity that passes through it? Why not connect it directly to the 12V GND? What benefits do I gain through passing it through the Arduino?
I know this is a hard one to wrap your head around - it used to always trip me up when i begin with microcontrollers (as i am from the software not hardware side)
Basically (repeat after me) GROUND is GROUND is GROUND is GROUND. 
It does not matter (there are some caveats) what the +ve voltage is - ground is always essentially Zero volts.
Craig