What is the correct procedure for operating the engine fire extinguishers on an ATR72?
As I understand it, pilot must pull the red handle and twist 90 degrees. This will stop the engine. Pilot must then press the discharge squib button in order to deploy the extinguishers. is this correct?


Yes, this is correct, except that the handle does not need to be twisted as far as I know. When the handle is pulled, the following things will happen:

The propeller on this side is feathered.
The fuel LP (low pressure) valve is closed.
The bleed air and HP valves are closed.
The deice and shutoff valve is closed.
The DC and ACW generators are disconnected.
The hydraulic to prop brake is closed on the other engine.

Pressing the squib button will then discharge the extinguishing bottle into the engine.



What would happen if the pilot pressed the discharge squib button before pulling the red handle?


Nothing, the button is not armed at this stage:

AGENT/SQUIB
armed when T handle pulled.
Discharges bottle.
(DC EMER/HOT MAIN BAT)




Am I correct in assuming that if the system has detected an engine fire, then the &quot;fault off&quot; buttons would be lit and there would be an audible alarm? If this is the case, would the alarm stop when the discharge squib button is pressed, or only when the fault off button is pressed?


Yes, both FAULT lights would be on and the alarm is triggered, if both loops A and B detect the fire:

The pilots would be alerted of the fire by:

master WARNING light flashes
ENG 1/2 FIRE light illuminates on the CAP (Crew Alerting Panel)
FUEL SO illuminates on the respective condition lever
respective fire handle illuminates
aural alarm sounds

A single FAULT would indicate a fault in the detection system, not a fire itself:

LOOP/FAULT
change in resistance, inhibits fire signal until turned off.
Loop on CAP (DC emer)

You would press the button to turn off the respective loop such that the other loop can detect a fire alone:

OFF
takes respective loop out of parallel circuit. Allows other loop to activate fire signal alone.




Above the buttons it is written: &quot;Agent 1 Loop A&quot; and &quot;Loop B Agent 2&quot;. what does this mean and what is the difference between the two systems? In what circumstances would the pilot have to press both discharge squib buttons or both fault off buttons? In what circumstances would they only have to press one?


There are two fire extinguishing bottles and each can be discharged into either engine (Agent 1 refers to the bottle on the same side and Agent 2 to the one on the other side):

The correct procedure for an IN FLIGHT ENG FIRE is:

PL [Power Lever] affected side ... FI [Flight Idle]
CL [Condition Lever] affected side ... FTR [Feather] THEN FUEL SO
FIRE HANDLE affected side ... PULL
if condition persists after 10 seconds:
AGENT 1 affected side ... DISCH
if condition persists after 30 seconds:
AGENT 2 affected side ... DISCH
LAND ASAP

(ATR 72 QRH)

Source: ATR Systems Training Document
Also have a look at this YouTube video found by Jpe61.